about the use of standard integration schemes for x fem in solid mechanics plasticity abstract the introduction of plasticity in an extended finite element x fem framework is very recent and arises several technical and scientific difficulties due to the moving position of integration points as the crack proceeds if a fixed grid is not used currently the existing analyses in plasticity with x fem are limited to monotonic plasticity approximated by non linear elasticity using the hrr field decomposition however such an analysis cannot be applied in fatigue where cyclic plasticity plays a major role in crack propagation the aim of this study is to tackle one of the difficulties induced by cyclic plastic computation the projection of the internal variables during crack propagation the discontinuous heaviside function in the elements cut by the crack is replaced by a new continuous enrichment function this new function is polynomial and its degrees and coefficients depend on the type of element and on the position of the interface in the element the automatic determination of the new enrichment and its introduction in a linear and non linear framework have been implemented for linear elements in two dimensions and three dimensions and tested with convergence tests in elasticity and plasticity

on the distribution of the peak to average power ratio in ofdm signals the distribution of the peak to average power ratio papr in strictly band limited orthogonal frequency division multiplexing ofdm signals is studied assuming that the base band ofdm signal is characterized as a band limited complex gaussian process we first attempt to derive the exact distribution of the papr in the band limited ofdm signals since this distribution cannot be expressed in a closed form we further develop a simple closed form approximation based on the level crossing rate analysis comparisons of the proposed distributions with those obtained by computer simulations show good agreement and convergence with an increase in the number of subcarriers

efficient isoparametric trimmed hexahedral elements with explicit shape functions abstract in this study we develop isoparametric trimmed hexahedral th elements with explicit shape functions for finite element analysis using trimmed meshes th elements are placed at the boundary of a trimmed mesh generated by cutting a regular hexahedral mesh with a geometric surface master th elements are defined based on the marching cubes algorithm for an isoparametric mapping from the reference coordinates to the physical coordinates shape function values at the support points of master th elements are precomputed by solving laplace s equation with appropriate boundary conditions explicit shape functions for master th elements are constructed by interpolating the precomputed shape function values at the support points of master th elements the present explicit shape functions satisfy the required properties of fem and significantly reduce the computational cost compared with the previously developed polyhedral shape functions

on the flexibility of agglomeration based physical space discontinuous galerkin discretizations in this work we show that the flexibility of the discontinuous galerkin dg discretization can be fruitfully exploited to implement numerical solution strategies based on the use of elements with very general shapes thanks to the freedom in defining the mesh topology we propose a new h adaptive technique based on agglomeration coarsening of a fine mesh the possibility to enhance the error distribution over the computational domain is investigated on a poisson problem with the goal of obtaining a mesh independent discretization the main building block of our dg method consists of defining discrete polynomial spaces directly on physical frame elements for this purpose we orthonormalize with respect to the l 2 product a set of monomials relocated in a specific element frame and we introduce an easy way to reduce the cost related to numerical integration on agglomerated meshes to complete the dg formulation for second order problems two extensions of the br2 scheme to arbitrary polyhedral grids including an estimate of the stabilization parameter ensuring the coercivity property are here proposed

quadratic serendipity finite elements over convex polyhedra summary the conventional approach to construct quadratic elements for an n sided polygon will yield n n 1 2 shape functions which increases the computational effort it is well known that the serendipity elements based on isoparametric formulation suffers from mesh distortion floater and lai proposed a systematic way to construct higher order approximations over arbitrary polygons using the generalized barycentric coordinates and triangular coordinates this approach ensures 2n shape functions with nodes only on the boundary of the polygon in this paper we extend the polygonal splines approach to three dimensions and construct serendipity shape functions over hexahedra and convex polyhedra this is done by expressing the shape functions using the barycentric coordinates and the local tetrahedral coordinates the quadratic shape functions possess kronecker delta property and satisfy constant linear and quadratic precision the accuracy and the convergence properties of the quadratic serendipity shape elements are demonstrated with a series of standard patch tests the numerical results show that the quadratic serendipity elements pass the patch test yield optimal convergence rate and can tolerate extreme mesh distortion this article is protected by copyright all rights reserved

a smoothed coupled ns nes fem for dynamic analysis of 2d fluid solid interaction problems abstract a node based smoothed finite element method ns fem t3 using triangular elements and a n sided polygonal edge based smoothed fem n es fem using polygonal elements is combined to give the smoothed coupled ns n es fem for dynamic analysis of two dimensional 2d fluid solid interaction problems based on the pressure displacement formulation in the present method the ns fem t3 is used for the fluid domain and the gradient of pressure is smoothed while the n es fem is used for the solid domain and the gradient of displacement is smoothed this gradient smoothing technique can provide proper softening effect which will effectively relieve the overly stiff behavior of the fem model and thus improve significantly the solution of coupled system some numerical examples have been presented to illustrate the effectiveness of the coupled ns n es fem compared with some existing methods for 2d fluid solid interaction problems

adaptively weighted numerical integration in the finite cell method abstract with adaptively weighted aw numerical integration for a given set of quadrature nodes order and domain of integration the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense the moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain and then are corrected for the deviation from the original domain using shape sensitivity analysis in this paper we demonstrate the application of aw integration scheme in the context of the finite cell method which must perform numerical integration over arbitrary domains without meshing the standard integration technique employed in fcm is the characteristic function method that converts the continuous integrand over a complex domain into a discontinuous integrand over a simple box domain then well known integrand adaptivity techniques are employed to integrate the resulting discontinuous integrand over the box domain although this method is simple to implement it becomes computationally very expensive for realistic complex 3d domains such as sculptures bones and engines in contrast in aw scheme the quadrature weights directly adapt to the complex geometric domain without the need to making the integrand discontinuous leading to superior computational properties in this paper we demonstrate the computational efficiency of aw over the characteristic function method as it requires fewer subdivisions and less time to achieve a given accuracy in both two and three dimensions in addition aw offers a number of advantages including flexibility in the choice of quadrature points and basis functions

a new polyhedral element for the analysis of hexahedral dominant finite element models and its application to nonlinear solid mechanics problems abstract a hexahedral dominant finite element mesh can be easily constructed by cutting regular hexahedral elements in a simple block with cad surfaces representing outer surfaces of a geometric model polyhedral elements with straight edges but possibly non planar faces are generated at the domain boundaries while regular hexahedral elements remain in the interior region shape functions for polyhedral elements are derived from moving least square approximation based on a tetrahedral subdivision of polyhedral domains by a centroid based subdivision technique the polyhedral shape functions in this study have similar properties to conventional finite element shape functions in terms of continuity and completeness within elements compatibility across inter element boundaries and the kronecker delta property furthermore the present approach using hexahedral dominant meshes with polyhedral elements at domain boundaries is successfully applied to solve large deformation problems of hyperelastic and elastic plastic materials

asymptotic limits in peak envelope power reduction by redundant coding in orthogonal frequency division multiplex modulation this paper uses some computational results to show that the peak envelope power pep of orthogonal frequency division multiplex ofdm waveforms can be reduced very substantially by coding to select only those messages with low peak factor as valid codewords in the scheme it is shown that the asymptotic limit of the pep is between two and three and that only four bits of redundancy are necessary to limit the pep to within 10 of this optimum value as the number of carriers becomes large

an efficient augmented finite element method for arbitrary cracking and crack interaction in solids summary this paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary multiple intra elemental discontinuities in 2d solids the augmented finite element method a fem employs four internal nodes to account for the crack displacements due to an intra elemental weak or strong discontinuity and it permits repeated elemental augmentation to include multiple interactive cracks it thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity and to multiple interactive cohesive cracks all within a single bilinear element that employs standard external nodal dofs only a novel elemental condensation procedure has been developed to solve the internal nodal dofs as functions of the external nodal dofs for any irreversible piece wise linear cohesive laws it leads to a fully condensed elemental equilibrium equation with mathematical exactness eliminating the need for nonlinear equilibrium iterations at elemental level the new a fem s high fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous and heterogeneous solids have been demonstrated through several challenging numerical examples it is shown that the proposed a fem empowered by the new elemental condensation procedure is numerically very efficient accurate and robust copyright 2014 john wiley sons ltd

on the computation and reduction of the peak to average power ratio in multicarrier communications for any code c defined over an equal energy constellation it is first shown that at any time instance the problem of determining codewords of c with high peak to average power ratios papr in a multicarrier communication system is intimately related to the problem of minimum distance decoding of c subsequently a method is proposed for computing the papr by minimum distance decoding of c at many points of time moreover an upper bound on the error between this computed value and the true one is derived analogous results are established for codes defined over arbitrary signal constellations as an application of this computational method an approach for reducing the papr of c proposed by jones and wilkinson 1996 is revisited this approach is based on introducing a specific phase shift to each coordinate of all the codewords where phase shifts are independent of the codewords and known both to the transmitter and the receiver we optimize the phase shifts offline by applying our method for computing the papr for the coding scenario proposed by the etsi bran standardization committee reductions of order 4 5 db can be freely obtained using the computed phase shifts examples are provided showing that most of the gain is preserved when the computed optimal phase shifts are rounded to quantenary phase shift keying psk 8 psk and 16 psk type phase shifts

symmetric quadrature rules on a triangle abstract we present a class of quadrature rules on triangles in r 2 which somewhat similar to gaussian rules on intervals in r 1 have rapid convergence positive weights and symmetry by a scheme combining simple group theory and numerical optimization we obtain quadrature rules of this kind up to the order 30 on triangles this scheme essentially a formalization and generalization of the approach used by lyness and jespersen over 25 years ago can be easily extended to other regions in r 2 and surfaces in higher dimensions such as squares spheres we present example formulae and relevant numerical results

symmetric gauss legendre quadrature formulas for composite numerical integration over a triangular surface abstract this paper first presents a gauss legendre quadrature method for numerical integration of i t f x y d x d y where f x y is an analytic function in x y and t is the standard triangular surface x y 0 x y 1 x y 1 in the cartesian two dimensional x y space we then use a transformation x x y y to change the integral i to an equivalent integral s f x y x y d d where s is now the 2 square in space 1 1 we then apply the one dimensional gauss legendre quadrature rules in and variables to arrive at an efficient quadrature rule with new weight coefficients and new sampling points we then propose the discretisation of the standard triangular surface t into n 2 right isosceles triangular surfaces t i i 1 1 n 2 each of which has an area equal to 1 2 n 2 units we have again shown that the use of affine transformation over each t i and the use of linearity property of integrals lead to the result i i 1 n n t i f x y d x d y 1 n 2 t h x y d x d y where h x y i 1 n n f x i x y y i x y and x x i x y and y y i x y refer to affine transformations which map each t i in x y space into a standard triangular surface t in x y space we can now apply gauss legendre quadrature formulas which are derived earlier for i to evaluate the integral i 1 n 2 t h x y d x d y we observe that the above procedure which clearly amounts to composite numerical integration over t and it converges to the exact value of the integral t f x y d x d y for sufficiently large value of n even for the lower order gauss legendre quadrature rules we have demonstrated this aspect by applying the above explained composite numerical integration method to some typical integrals

higher order extended finite elements with harmonic enrichment functions for complex crack problems summary in this paper we analyze complex crack problems in elastic media using harmonic enrichment functions in a higher order extended finite element implementation the numerically computed enrichment function of a crack is the solution of the laplace equation with discontinuous dirichlet boundary condition along the crack and its interaction with branches or other cracks is realized by imposing vanishing neumann boundary conditions along those cracks the classical finite element displacement approximation is enriched by adding the enrichment function of a crack through the framework of partition of unity a nested subgrid mesh is used in the laplace solve with a rasterized approximation of a crack which simplifies the numerical integration no partitioning of finite elements is required harmonic enrichment functions readily permit the extension to handle multiple interacting and branched cracks without any special treatment around the junction points several numerical examples are presented that arm the accuracy and eectiveness of the method when applied to complex crack

representation of singular fields without asymptotic enrichment in the extended finite element method summary in this paper we replace the asymptotic enrichments around the crack tip in the extended finite element method xfem with the semi analytical solution obtained by the scaled boundary finite element method sbfem the proposed method does not require special numerical integration technique to compute the stiffness matrix and it improves the capability of the xfem to model cracks in homogeneous and or heterogeneous materials without a priori knowledge of the asymptotic solutions a heaviside enrichment is used to represent the jump across the discontinuity surface we call the method as the extended sbfem numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics show that the proposed method yields accurate results with improved condition number a simple code is annexed to compute the terms in the stiffness matrix which can easily be integrated in any existing fem xfem code copyright 2013 john wiley sons ltd

polygonal finite element a comparison of the stiffness matrix integration methods abstract this paper aims to determine which numerical integration method shows the best performance when integrating the polygonal finite element stiffness matrix hence numerical comparisons were made between two existing methods triangulation and quadrangulation and two new quadrature rules developed by the authors called polygonal gauss legendre quadrature pgl and rational polynomial gauss quadrature rpg in this study pgl 1 points and weights were obtained for polynomials of degree 3 5 6 8 and 9 while rpg 2 rules were calculated for rational polynomials of degree 8 8 10 8 and 16 16 briefly the pgl rule showed the best performance reducing the execution time in 38 6 at best compared with the triangulation also its implementation is much more straightforward

a paradigm for higher order polygonal elements in finite elasticity using a gradient correction scheme abstract recent studies have demonstrated that polygonal elements possess great potential in the study of nonlinear elastic materials under finite deformations on the one hand these elements are well suited to model complex microstructures e g particulate microstructures and microstructures involving different length scales and incorporating periodic boundary conditions on the other hand polygonal elements are found to be more tolerant to large localized deformations than the standard finite elements and to produce more accurate results in bending and shear with mixed formulations lower order mixed polygonal elements are also shown to be numerically stable on voronoi type meshes without any additional stabilization treatment however polygonal elements generally suffer from persistent consistency errors under mesh refinement with the commonly used numerical integration schemes as a result non convergent finite element results typically occur which severely limit their applications in this work a general gradient correction scheme is adopted that restores the polynomial consistency by adding a minimal perturbation to the gradient of the displacement field with the correction scheme the recovery of optimal convergence for solutions of displacement based and mixed formulations with both linear and quadratic displacement interpolants is confirmed by numerical studies of several boundary value problems in finite elasticity in addition for mixed polygonal elements the various choices of the pressure field approximations are discussed and their performance on stability and accuracy are numerically investigated we present applications of those elements in physically based examples including a study of filled elastomers with interphasial effect and a qualitative comparison with cavitation experiments for fiber reinforced elastomers

a numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions we present a numerical algorithm for the construction of efficient high order quadratures in two and higher dimensions quadrature rules constructed via this algorithm possess positive weights and interior nodes resembling the gaussian quadratures in one dimension in addition rules can be generated with varying degrees of symmetry adaptable to individual domains we illustrate the performance of our method with numerical examples and report quadrature rules for polynomials on triangles squares and cubes up to degree 50 these formulae are near optimal in the number of nodes used and many of them appear to be new

a stress displacement virtual element method for plane elasticity problems abstract the numerical approximation of 2d elasticity problems is considered in the framework of the small strain theory and in connection with the mixed hellinger reissner variational formulation a low order virtual element method vem with a priori symmetric stresses is proposed several numerical tests are provided along with a rigorous stability and convergence analysis

symmetric numerical integral formulas for regular polygons the theory of interpolatory integration formulas in n dimensions is combined with group theory to classify and generate symmetric integration formulas in a systematic way the points are computed as the common zeros of a set of polynomials these polynomials constitute a canonical basis for the real ideal belonging to the formula for a symmetric formula they can be chosen to span a representation of the symmetry group for regions with high symmetry and formulas of low degree this leads to only a few distinct possibilities and the existence of the corresponding formulas is easily checked in general however the canonical basis is not completely determined by symmetry and degree and a suitable choice has to be made the application to regular polygons in two dimensions is discussed and formulas are presented for polygons with three five six seven and eight vertices with varying degrees of exactness up to order 27 for the hexagon

symmetric triangle quadrature rules for arbitrary functions abstract despite extensive research on symmetric polynomial quadrature rules for triangles as well as approaches to their calculation few studies have focused on non polynomial functions particularly on their integration using symmetric triangle rules in this paper we present two approaches to computing symmetric triangle rules for singular integrands by developing rules that can integrate arbitrary functions the first approach is well suited for a moderate amount of points and retains much of the efficiency of polynomial quadrature rules the second approach better addresses large amounts of points though it is less efficient than the first approach we demonstrate the effectiveness of both approaches on singular integrands which can often yield relative errors two orders of magnitude less than those from polynomial quadrature rules

a finite element method with mesh separation based approximation technique and its application in modeling crack propagation with adaptive mesh refinement summary this paper presents a fem with mesh separation based approximation technique that separates a standard element into three geometrically independent elements a dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation the novel technique makes it very easy for mesh generation of problems with complex or solution dependent varying geometry it offers a flexible way to construct displacement approximations and provides a unified framework for the fem to enjoy some of the key advantages of the hansbo and hansbo method the meshfree methods the semi analytical fems and the smoothed fem for problems with evolving discontinuities the method enables the devising of an efficient crack tip adaptive mesh refinement strategy to improve the accuracy of crack tip fields both the discontinuities due to intra element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level the effectiveness and robustness of the present method are benchmarked with several numerical examples the numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test and it is essential to apply local adaptive mesh refinement for low fracture energy problems copyright 2014 john wiley sons ltd

algebraic cubature on polygonal elements with a circular edge abstract we compute low cardinality algebraic cubature formulas on convex or concave polygonal elements with a circular edge by subdivision into circular quadrangles blending formulas via subperiodic trigonometric gaussian quadrature and final compression via caratheodory tchakaloff subsampling of discrete measures we also discuss applications to the vem virtual element method in computational mechanics problems

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

adaptively weighted numerical integration over arbitrary domains abstract in adaptively weighted numerical integration for a given set of quadrature nodes order and domain of integration the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense the moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain and then are corrected for the deviation from the original domain using shape sensitivity analysis using divergence theorem the moments reduce to integrals over the boundary of the simplified domain the proposed approach supports accurate and efficient computation of quadrature weights for integration of a priori unknown functions over arbitrary 2d and 3d solid domains experimental results 2d indicate that adaptively weighted integration compares favorably with more traditional approaches because the adaptively weighted integration avoids excessive domain subdivision it is useful in many applications and meshfree analysis in particular

extended finite element method on polygonal and quadtree meshes in this paper we present mesh independent modeling of discontinuous flelds on polygonal and quadtree flnite element meshes this approach falls within the class of extended and generalized flnite element methods where the partition of unity framework is used to introduce additional enrichment functions within the classical displacement based flnite element approximation for crack modeling a discontinuous function and the two dimensional asymptotic crack tip flelds are used as enrichment functions linearly complete partition of unity approximations are adopted on polygonal convex and nonconvex elements and quadtree meshes excellent agreement with reference solution results is obtained for mixed mode stress intensity factors on benchmark crack problems and crack growth simulations without remeshing are conducted on polygonal and quadtree meshes to reveal the potential of the proposed techniques in computational failure mechanics

higher order extended fem for weak discontinuities level set representation quadrature and application to magneto mechanical problems in this article we present the application of bilinear and biquadratic extended fem xfem formulations to model weak discontinuities in magnetic and coupled magneto mechanical boundary value problems for properly resolving the location of curved interfaces and the discontinuous physical behaviour the major part of the contribution is devoted to review and develop methods for level set representation of curved interfaces and numerical integration of the weak form in higher order xfem formulations in order to reduce the complexity of the representation of curved interfaces an element local approach that allows for an automated computation of the level set values and also improves the compatibility between the level set representation and the integration subdomains is proposed integration rules for polygons and strain smoothing are applied in conjunction with biquadratic elements and compared with curved integration subdomains eventually a coupled magneto mechanical demonstration problem is modelled and solved by xfem for demonstration purposes a magneto mechanical coupling due to magnetic stresses is considered errors and convergence rates are analysed for the different level set representations and numerical integration procedures as well as their dependence on the ratio of material parameters at an interface copyright c 2012 john wiley sons ltd

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

gaussian quadrature for c1 cubic clough tocher macro triangles abstract a numerical integration rule for multivariate cubic polynomials over n dimensional simplices was designed by hammer and stroud 1956 the quadrature rule requires n 2 quadrature points the barycentre of the simplex and n 1 points that lie on the connecting lines between the barycentre and the vertices of the simplex in the planar case this particular rule belongs to a two parameter family of quadrature rules that admit exact integration of bivariate polynomials of total degree three over triangles we prove that this rule is exact for a larger space namely the c 1 cubic clough tocher spline space over macro triangles if and only if the split point is the barycentre this results in a factor of three reduction in the number of quadrature points needed to integrate the clough tocher spline space exactly

generalized gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method new gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method for discontinuous functions we construct gauss like quadrature rules over arbitrarily shaped elements in two dimensions without the need for partitioning the finite element a point elimination algorithm is used in the construction of the quadratures which ensures that the final quadratures have minimal number of gauss points for weakly singular integrands we apply a polar transformation that eliminates the singularity so that the integration can be performed efficiently and accurately numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques

generalized gaussian quadrature rules on arbitrary polygons in this paper we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons these quadratures have desirable properties such as positivity of weights and interiority of nodes and can readily be used as software libraries where numerical integration within planar polygons is required we have used this algorithm for the construction of symmetric and non symmetric quadrature rules over convex and concave polygons while in the case of symmetric quadratures our results are comparable to available rules the proposed algorithm has the advantage of being flexible enough so that it can be applied to arbitrary planar regions for the integration of generalized classes of functions to demonstrate the efficiency of the new quadrature rules we have tested them for the integration of rational polygonal shape functions over a regular hexagon for a relative error of 10 8 in the computation of stiffness matrix entries one needs at least 198 evaluation points when the region is partitioned whereas 85 points suffice with our quadrature rule copyright 2009 john wiley sons ltd

polygonal finite elements for topology optimization a unifying paradigm in topology optimization literature the parameterization of design is commonly carried out on uniform grids consisting of lagrangian type finite elements e g linear quads these formulations however suffer from numerical anomalies such as checkerboard patterns and one node connections which has prompted extensive research on these topics a problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members leading to mesh dependent sub optimal designs thus to address the geometric features of the spatial discretization we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions more specifically we consider polygonal meshes constructed from voronoi tessellations which in addition to possessing higher degree of geometric isotropy allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities copyright 2009 john wiley sons ltd

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 john wiley sons ltd

harmonic enrichment functions a unified treatment of multiple intersecting and branched cracks in the extended finite element method a unifying procedure to numerically compute enrichment functions for elastic fracture problems with the extended finite element method is presented within each element that is intersected by a crack the enrichment function for the crack is obtained via the solution of the laplace equation with dirichlet and vanishing neumann boundary conditions a single algorithm emanates for the enrichment field for multiple cracks as well as intersecting and branched cracks without recourse to special cases which provides flexibility over the existing approaches in which each case is treated separately numerical integration is rendered to be simple there is no need for partitioning of the finite elements into conforming subdivisions for the integration of discontinuous or weakly singular kernels stress intensity factor computations for different crack configurations are presented to demonstrate the accuracy and versatility of the proposed technique copyright 2010 john wiley sons ltd

polynomial interpolation and cubature over polygons we have implemented a matlab code to compute discrete extremal sets of fekete and leja type on convex or concave polygons together with the corresponding interpolatory cubature formulas the method works by qr and lu factorizations of rectangular vandermonde matrices on weakly admissible meshes wams of polygons constructed by polygon quadrangulation

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

computing almost minimal formulas on the square the main purpose of this paper is to introduce a numerical method for the computation of cubature rules on the square 1 1 2 that are almost minimal i e with few points w r t the degree of precision d in particular for all email protected email protected 55 the sets x d and the weights w k are new new rules are also achieved for degrees 15 d 17 19 and d 23 respectively with 43 54 67 and 96 points

hierarchical a posteriori error estimators for the mimetic discretization of elliptic problems we present an a posteriori error estimate of hierarchical type for the mimetic discretization of elliptic problems under a saturation assumption the global reliability and efficiency of the proposed a posteriori estimator are proved several numerical experiments assess the actual performance of the local error indicators in driving adaptive mesh refinement algorithms based on different marking strategies finally we analyze and test an inexpensive variant of the proposed error estimator which drastically reduces the overall computational cost of the adaptive procedures

a family of virtual element methods for plane elasticity problems based on the hellinger reissner principle abstract in the framework of 2d elasticity problems a family of virtual element schemes based on the hellinger reissner variational principle is presented a convergence and stability analysis is rigorously developed numerical tests confirming the theoretical predictions are performed

first and second passage times of rayleigh processes corresp the first and second passage times of a stationary rayleigh process r t a are discussed r t a represents the envelope of a stationary random process consisting of a sinusoidal signal of amplitude and frequency f 0 plus stationary gaussian noise of unit variance having a narrow band power spectral density which is symmetrical about f 0 approximate integral equations are developed whose solutions yield approximate probability densities concerning the first and second passage times of r t a the resulting probability functions are presented in graphs for the case when the power spectral density of the noise is gaussian related results concerning the approximate distribution function of the absolute minimum or absolute maximum of r t a in the closed interval 0 tau are also presented the exact probability densities are expressed in the form of an infinite series of multiple integrals

on the phase sequence set of slm ofdm scheme for a crest factor reduction the crest factor distribution of orthogonal frequency division multiplexing ofdm symbol sequences is evaluated and it is shown that ofdm symbol sequences with a short period are expected to have a high crest factor the crest factor relationship between two input symbol sequences hamming distance d apart is also derived using these two results two criteria are proposed for a phase sequence set of the selected mapping slm ofdm scheme and suggest the rows of the cyclic hadamard matrix constructed from an m sequence as a near optimal phase sequence set of the slm ofdm scheme

on numerical quadrature for c1 quadratic powell sabin 6 split macro triangles abstract the quadrature rule of hammer and stroud 1956 for cubic polynomials has been shown to be exact for a larger space of functions namely the c 1 cubic clough tocher spline space over a macro triangle if and only if the split point is the barycentre of the macro triangle kosinka and barto 2018 we continue the study of quadrature rules for spline spaces over macro triangles now focusing on the case of c 1 quadratic powell sabin 6 split macro triangles we show that the 3 node gaussian quadrature s for quadratics can be generalised to the c 1 quadratic powell sabin 6 split spline space over a macro triangle for a two parameter family of inner split points not just the barycentre as in kosinka and barto 2018 the choice of the inner split point uniquely determines the positions of the edge split points such that the whole spline space is integrated exactly by a corresponding polynomial quadrature consequently the number of quadrature points needed to exactly integrate this special spline space reduces from twelve to three for the inner split point at the barycentre we prove that the two 3 node quadratic polynomial quadratures of hammer and stroud exactly integrate also the c 1 quadratic powell sabin spline space if and only if the edge split points are at their respective edge midpoints for other positions of the inner and edge split points we provide numerical examples showing that three nodes suffice to integrate the space exactly but a full classification and a closed form solution in the generic case remain elusive

on the peak to average power of ofdm signals based on oversampling orthogonal frequency division multiplexing ofdm introduces large amplitude variations in time which can result in significant signal distortion in the presence of nonlinear amplifiers we introduce a new bound for the peak of the continuous envelope of an ofdm signal based on the maximum of its corresponding oversampled sequence it is shown to be very tight as the oversampling rate increases the bound is then used to derive a closed form probability upper bound for the complementary cumulative distribution function of the peak to mean envelope power ratio of uncoded ofdm signals for sufficiently large numbers of subcarriers as another application of the bound for oversampled sequences we propose tight relative error bounds for computation of the peak power using two main methods the oversampled inverse fast fourier transform and the method introduced for coded systems based on minimum distance decoding of the code

3d corrected xfem approach and extension to finite deformation theory in this paper the modified or corrected extended finite element method originally presented in fries int j numer meth engng 2008 75 503 532 for the 2d case is extended to 3d including different remedies for the problem that the crack front enrichment functions are linearly dependent in the blending elements in the context of this extension we address a number of computational issues of the 3d xfem in particular possible quadrature rules for elements with discontinuities also the influence of finite deformation theory for crack simulations in comparison to linear elastic fracture mechanics is investigated a number of numerical examples demonstrate the behavior of the presented possibilities copyright 2010 john wiley sons ltd

on the application of the method of difference potentials to linear elastic fracture mechanics the difference potential method dpm proved to be a very efficient tool for solving boundary value problems bvps in the case of complex geometries it allows bvps to be reduced to a boundary equation without the knowledge of green s functions the method has been successfully used for solving very different problems related to the solution of partial differential equations however it has mostly been considered in regular lipschitz domains in the current paper for the first time the method has been applied to a problem of linear elastic fracture mechanics this problem requires solving bvps in domains containing cracks for the first time dpm technology has been combined with the finite element method singular enrichment functions such as those used within the extended finite element formulations are introduced into the system in order to improve the approximation of the crack tip singularity near optimal convergence rates are achieved with the application of these enrichment functions for the dpm the reduction of the bvp to a boundary equation is based on generalised surface projections the projection is fully determined by the clear trace in the current paper for the first time the minimal clear trace for such problems has been numerically realised for a domain with a cut key words method of difference potentials extended finite element method fracture rate of convergence

quadrature rules for triangular and tetrahedral elements with generalized functions quadrature rules are developed for exactly integrating products of polynomials and generalized functions over triangular and tetrahedral domains these quadrature rules greatly simplify the implementation of finite element methods that involve integrals over volumes and interfaces that are not coincident with the element boundaries specifically the integrands considered here consist of a quadratic polynomial multiplied by a heaviside or dirac delta function operating on a linear polynomial this form allows for exact integration of expressions obtained from linear finite elements over domains and interfaces defined by a linear level set function exact quadrature rules are derived that involve fixed quadrature point locations with weights that depend continuously on the nodal level set values compared with methods involving explicit integration over subdomains the quadrature rules developed here accommodate degenerate interface geometries without any need for special consideration and provide analytical jacobian information describing the dependence of the integrals on the nodal level set values the accuracy of the method is demonstrated for a simple conduction problem with the neumann and robin type boundary conditions copyright 2007 john wiley sons ltd

generalized gaussian quadrature rules for systems of arbitrary functions a numerical algorithm is presented for the construction of generalized gaussian quadrature rules originally introduced by s karlin and w studden over three decades ago the quadrature rules to be discussed possess most of the desirable properties of the classical gaussian integration formulae such as positivity of the weights rapid convergence mathematical elegance etc the algorithm is applicable to a wide class of functions including smooth functions not necessarily polynomials as well as functions with end point singularities such as those encountered in the solution of integral equations complex analysis potential theory and several other areas the performance of the algorithm is illustrated with several numerical examples

a scaled boundary polygon formulation for elasto plastic analyses this study presents a novel scaled boundary polygon formulation to model elasto plastic material responses in structures the polygons have flexible mesh generation capabilities and are more accurate than standard finite elements especially for problems with cracks and notches shape functions of arbitrary n sided polygons are constructed using the scaled boundary finite element method these shape functions are conforming and linearly complete when modeling a crack strain singularities are analytically modeled without enrichment standard finite element procedures are used to formulate the stiffness matrix and residual load vector the nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function the stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present standard nonlinear equation solvers e g the modified newton raphson algorithm are used to obtain the nonlinear response of the structure the proposed formulation is validated using several numerical benchmarks

katetov s problem in 1948 miroslav katetov showed that if the cube x 3 of a compact space x satisfies the separation axiom t 5 then x must be metrizable he asked whether x 3 can be replaced by x 2 in this metrization result in this note we prove the consistency of this implication

an accurate robust and easy to implement method for integration over arbitrary polyhedra application to embedded interface methods we present an accurate method for the numerical integration of polynomials over arbitrary polyhedra using the divergence theorem the method transforms the domain integral into integrals evaluated over the facets of the polyhedra the necessity of performing symbolic computation during such transformation is eliminated by using one dimensional gauss quadrature rule the facet integrals are computed with the help of quadratures available for triangles and quadrilaterals numerical examples in which the proposed method is used to integrate the weak form of the navier stokes equations in an embedded interface method eim are presented the results show that our method is as accurate and generalized as the most widely used volume decomposition based methods moreover since the method involves neither volume decomposition nor symbolic computations it is much easier for computer implementation also the present method is more efficient than other available integration methods based on the divergence theorem efficiency of the method is also compared with the volume decomposition based methods and moment fitting methods to our knowledge this is the first article that compares both accuracy and computational efficiency of methods relying on volume decomposition and those based on the divergence theorem

polygonal finite element methods for contact impact problems on non conformal meshes in this paper a polygonal finite element method is presented for large deformation frictionless dynamic contact impact problems with non conformal meshes the geometry and interfaces of the problem are modeled independent of the background mesh based on the level set method to produce polygonal elements at the intersection of the interface with the regular fe mesh various polygonal shape functions are employed to investigate the capability of polygonal fem technique in modeling frictionless contact impact problems the contact constraints are imposed between polygonal elements produced along the contact surface through the node to surface contact algorithm several contact impact problems are modeled using various polygonal interpolation functions including the wachspress interpolation functions the metric coordinate shape functions the natural neighbor based functions and the mean value coordinate functions to demonstrate the efficiency of proposed technique in modeling contact impact problems

a novel scheme to generate meshes with hexahedral elements and poly pyramid elements the carving technique abstract a novel scheme for three dimensional mesh generation termed the carving technique is proposed with the aid of poly pyramid elements soaking the geometry information of a given model into a regular reference mesh with brick elements the reference mesh is trimmed by the surface of the model using the marching cube algorithm the trimmed elements are reconstructed by the proposed elements which here are termed the poly pyramid elements therefore the finite element mesh is automatically generated from the surface information shape functions of the poly pyramid elements are constructed by moving least square mls approximation numerical results are presented to examine the performance of the poly pyramid elements and to demonstrate the effectiveness of the proposed scheme

virtual and smoothed finite elements a connection and its application to polygonal polyhedral finite element methods summary we show both theoretically and numerically a connection between the smoothed finite element method sfem and the virtual element method and use this approach to derive stable cheap and optimally convergent polyhedral fem we show that the stiffness matrix computed with one subcell sfem is identical to the consistency term of the virtual element method irrespective of the topology of the element as long as the shape functions vary linearly on the boundary using this connection we propose a new stable approach to strain smoothing for polygonal polyhedral elements where instead of using sub triangulations we are able to use one single polygonal polyhedral subcell for each element while maintaining stability for a similar number of degrees of freedom the proposed approach is more accurate than the conventional sfem with triangular subcells the time to compute the stiffness matrix scales with the o dofs 1 1 in case of the conventional polygonal fem while it scales as o dofs 0 7 in the proposed approach the accuracy and the convergence properties of the sfem are studied with a few benchmark problems in 2d and 3d linear elasticity copyright 2015 john wiley sons ltd

the partitioned element method in computational solid mechanics abstract a finite element like approximation method is proposed for solid mechanics applications in which the elements can take essentially arbitrary polygonal form a distinguishing feature of the method herein called the partitioned element method is a partitioning of the elements into quadrature cells over which the shape functions are taken to be piecewise linear the gradient and constant values for each cell are determined by minimizing a quadratic function which represents a combined smoothness and compatibility measure linear completeness of the shape function formulation is proved robustness in the presence of element non convexity and geometric degeneracy e g nearly coincident nodes are particular goals of the method convergence for various 2d linear elasticity problems is demonstrated and results for a finite deformation elastic plastic problem are compared to those of the standard fem