fast and accurate computation of hypersingular integrals in galerkin surface integral equation formulations via the direct evaluation method hypersingular 4 d integrals arising in the galerkin discretization of surface integral equation formulations are computed by means of the direct evaluation method the proposed scheme extends the basic idea of the singularity cancellation methods usually employed for the regularization of the singular integral kernel by utilizing a series of coordinate transformations combined with a reordering of the integrations the overall algebraic manipulation results in smooth 2 d integrals that can be easily evaluated via standard quadrature rules finally the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency

arma parameter estimation using only output cumulants several algorithms are developed to estimate the parameters of a causal nonminimum phase autoregressive moving average arma p q system which is excited by an unobservable independently identically distributed non gaussian process the output is contaminated by additive colored gaussian noise of unknown power spectral density a fundamental result is presented pertaining to the identifiability of ar parameters based on the yule walker equations drawn from a specific set of p 1 1 d slices of the kth k 2 order output cumulant several ma parameter estimation algorithms are developed one method uses q 1 d slices of the output cumulant a second method uses only two 1 d cumulant slices these methods do not involve computation of the residual i e ar compensated time series or polynomial factorization multidimensional versions of the various algorithms are presented a simulation study demonstrating the effectiveness of the algorithms is included

extra dof free and linearly independent enrichments in gfem abstract a gfem without extra dof is developed without the extra dof the resulting linear system becomes independent in size of the order of local approximation the resulting pu approximation becomes free of linear dependence and the resulting stiffness matrix becomes good conditioned numerical studies show the new gfem s excellent convergence properties and excellent stability

implicit solution of the unsteady euler equations for high order accurate discontinuous galerkin discretizations efficient solution techniques for high order accurate time dependent problems are investigated for solving the two dimensional non linear euler equations in this work the spatial discretization consists of a high order accurate discontinuous galerkin dg approach implicit time integration techniques are considered exclusively in order to avoid the stability restrictions of explicit methods standard backwards differencing methods bdf1 and bdf2 as well as a second order crank nicholson cn2 and a fourth order implicit runge kutta irk4 scheme are considered in an attempt to balance the spatial and temporal accuracy of the overall approach the implicit system arising at each time step is solved using a p multigrid approach which is shown to produce h independent convergence rates while remaining relatively insensitive to the time step size the crank nicholson methodology although not l stable demonstrates superior performance compared to the bdf2 scheme for the problems chosen in this work however the fourth order accurate implicit runge kutta scheme is found to be the most efficient in terms of computational cost for a given accuracy level as compared to the lower order schemes in spite of the added cost per time step and the benefits of this scheme increase for tighter error tolerances

spectral element method for elastic and acoustic waves in frequency domain numerical techniques in time domain are widespread in seismic and acoustic modeling in some applications however frequency domain techniques can be advantageous over the time domain approach when narrow band results are desired especially if multiple sources can be handled more conveniently in the frequency domain moreover the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain in this paper we present a spectral element method sem in frequency domain to simulate elastic and acoustic waves in anisotropic heterogeneous and lossy media the sem is based upon the finite element framework and has exponential convergence because of the use of gll basis functions the anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems compared with the conventional finite element method the number of unknowns in the sem is significantly reduced and higher order accuracy is obtained due to its spectral accuracy to account for the acoustic solid interaction the domain decomposition method ddm based upon the discontinuous galerkin spectral element method is proposed numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain

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

partial regularity for subquadratic parabolic systems under controllable growth conditions in this paper we prove a regularity result for weak solutions away from singular set of parabolic systems with subquadratic growth condition of the type tu z diva z u du b z u du for z x t where the structure function a satisfies standard ellipticity and growth condition with polynomial growth rate 2nn 2 p 2 the inhomogeneity b satisfies the controllable growth condition b z u du 1 u p 1 du p 1 1p where p n 2 pn 2 p if n 2 p here p can be any exponent if n 2 p the proof is based on the a caloric approximation lemma to parabolic systems with subquadratic growth

the method of a harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition in this paper we consider the nonlinear elliptic systems under controllable growth condition we use a new method introduced by duzaar and grotowski for proving partial regularity for weak solutions based on a generalization of the technique of harmonic approximation we extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition and directly establishing the optimal holder exponent for the derivative of a weak solution

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

symmetric quadrature rules for tetrahedra based on a cubic close packed lattice arrangement a family of quadrature rules for integration over tetrahedral volumes is developed the underlying structure of the rules is based on the cubic close packed ccp lattice arrangement using 1 4 10 20 35 and 56 quadrature points the rules are characterized by rapid convergence positive weights and symmetry each rule is an optimal approximation in the sense that lower order terms have zero contribution to the truncation error and the leading order error term is minimized quadrature formulas up to order 9 are presented with relevant numerical examples

volumetric testing parallel to the boundary surface for a nonconforming discretization of the electric field integral equation the volumetric monopolar rwg discretization of the electric field integral equation efie imposes no continuity constraint across edges in the surface discretization around a closed conductor the current is expanded with the monopolar rwg set and the electric field is tested over a set of tetrahedral elements attached to the boundary surface this scheme is facet oriented and therefore well suited for the scattering analysis of nonconformal meshes or composite objects the observed accuracy though is only competitive with respect to the rwg discretization for a restricted range of heights of the tetrahedral elements in this communication we introduce a novel implementation of the volumetric monopolar rwg discretization of the efie with testing over a set of wedges we show with rcs and near field results that this scheme offers improved accuracy for a wider range of heights than the approach with tetrahedral testing the application of the wedge testing to the even surface odd volumetric monopolar rwg discretization of the efie edge oriented and therefore less versatile shows similar accuracy as with tetrahedral testing which is a sign of robustness

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

a finite element semi lagrangian method with l2 interpolation summary high order accurate methods for convection dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy the state of the art in this field is more advanced for eulerian methods than for semi lagrangian slag methods in this paper we introduce a new slag method that is based on combining the modified method of characteristics with a high order interpolating procedure the method employs the finite element method on triangular meshes for the spatial discretization an l2 interpolation procedure is developed by tracking the feet of the characteristic lines from the integration nodes numerical results are illustrated for a linear advection diffusion equation with known analytical solution and for the viscous burgers equation the computed results support our expectations for a robust and highly accurate finite element slag method copyright 2012 john wiley sons ltd

partial regularity for subquadratic homogeneity elliptic system with vmo coefficients abstract in this paper we are concerned with subquadratic homogeneity elliptic problems with vmo coefficients in divergence form we obtain that the weak solution u is locally holder continuous besides a singular set by using a harmonic approximation where the holder exponent 0 1 the hausdorff dimension of the singular set is less than n p

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

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

implicit runge kutta methods for the discretization of time domain integral equations implicit runge kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory the proposed technique maps a laplace domain equation to a domain equation using the butcher tableau of the implicit runge kutta scheme a discrete time domain system is recovered by computing the inverse transform numerically the resulting technique is capable of third or fifth order accuracy in time and is stable independent of time step numerical results illustrate the accuracy and stability of the technique

on the application of two symmetric gauss legendre quadrature rules for composite numerical integration over a triangular surface this paper first presents a gauss legendre quadrature rule for the evaluation 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 two space x y we transform this integral into an equivalent integral s f x y frac x y d d where s is 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 rules with new weight coefficients and new sampling points then a second gauss legendre quadrature rule of composite type is obtained this rule is derived by discretising t into three new triangles tic i 1 2 3 of equal size which are obtained by joining centroid of t c 1 3 1 3 to the three vertices of t by use of affine transformations defined over each tic and the linearity property of integrals leads to the result i underover i 1 3 tic f x y d x d y frac 1 3 t g x y d x d y where g x y i 1n n f xic x y yic x y and x xic x y and y yic x y refer to affine transformations which map each tic into t the standard triangular surface we then write t g x y d x d y s g x y frac x y d d and a composite rule of integration is thus obtained we next propose the discretisation of the standard triangular surface t into n2 right isosceles triangular surfaces ti i 1 1 n2 each of which has an area equal to 1 2 n2 units we have again shown that the use of affine transformation over each ti and the use of linearity property of integrals lead to the result t f x y d x d y underover i 1 n n ti f x y d x d y frac 1 n2 t h x y d x d y where h x y i 1n n f xi x y yi x y and x xi x y y yi x y refer to affine transformations which map each ti in x y space into t a standard triangular surface t in the x y space we can now apply the two rules earlier derived to the integral t h x y d x d y this amounts to application of composite numerical integration of t into n2 and 3n2 triangles of equal sizes respectively we can now apply the rules which are derived earlier to the evaluation of the integral t f x y d x d y and each of these procedures converges to the exact value of the integral t f x y d x d y for sufficiently large value of n and the convergence is much faster for higher order rules we have demonstrated this aspect by applying the above composite integration method to some typical integrals 2007 elsevier inc all rights reserved

indirect finite element evaluation of two dimensional finite part integral using fourier transformation a broad class of engineering problems in fracture mechanics thermal fluid transport and electromagnetic theory involve the evaluation of two dimensional finite part integrals of the form a method for evaluation of such integrals is developed by deriving an equivalent integral using fourier transformation this equivalent integral does not involve a kernel with singular behaviour consequently standard numerical integration methodologies with conventional analytical evaluation techniques can be used in the finite element computations the accuracy and convergence of the developed numerical procedure are successfully demonstrated by numerical examples for planar fracture geometries

the mini mixed finite element for the stokes problem an experimental investigation abstract o h 3 2 superconvergence in pressure and velocity has been experimentally investigated for the two dimensional stokes problem discretized with the mini mixed finite element even though the classic mixed finite element theory for the mini element guarantees linear convergence for the total error recent theoretical results indicate that superconvergence of order o h 3 2 in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured three directional triangular meshes the numerical experiments presented here suggest a more general validity of o h 3 2 superconvergence possibly to automatically generated and unstructured triangulations in addition the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise linear part of the computed velocity finding that the former is generally closer to the exact velocity whereas the latter conserves mass better

an accurate approach for the calculation of mom matrix elements the method of moments solution on integral equations for electromagnetic scattering and radiation problems with rao wilton glisson rwg and n spl times rwg basis functions requires the calculation of singular double surface integrals over triangular subdomains in this paper an approach is presented to deal with the singularity and almost singularity in which the triangle subdomain is divided into several subtriangles and then the singular or almost singular integral is calculated over each of the subtriangles this approach is mainly based on the projection process and the local polar frame it can be used to deal with the singular double surface integrals of order 1 r and 1 r sup 2 in which vector functions may be of zeroth order and higher order numerical examples are provided to verify the validity of the method presented in this paper for dealing with the singularity and almost singularity

adjoint sensitivity formulation for discontinuous galerkin discretizations in unsteady inviscid flow problems this paper presents an unsteady discrete adjoint algorithm for high order implicit discontinuous galerkin discretizations in time dependent inviscid flow problems the major function of the adjoint approach is to obtain the sensitivity information in a time dependent functional output which in turn is used to drive an unsteady shape optimization process to deliver a minimum of the objective functional a gradient based optimization strategy is investigated in which the sensitivity derivatives of the objective functional with respect to input variables are formulated in the context of high order discontinuous galerkin discretizations while special emphasis is given to the variations and linearizations of curvilinear boundary elements implicit temporal discretizations consisting of a second order backward euler scheme and a fourth order implicit runge kutta scheme are considered exclusively in this work where the corresponding adjoint problem is required to be solved in a backward time integration manner due to the associated transpose operation two numerical examples for the unsteady shape design techniques are presented to verify the derived sensitivity formulations and to demonstrate the performance of the adjoint approach the first involves an inverse shape optimization case by matching a time dependent target pressure profile for a two dimensional periodic vortical gust impinging on a rae 2822 airfoil and the second considers minimization of the acoustic noise produced by subsonic flow over a naca0012 airfoil with a 0 03c thick blunt trailing edge

a novel recursive approach to estimating ma parameters of causal arma models from cumulants the estimation of ma moving average parameters of causal arma autoregressive moving average models using the third order cumulants alone is treated a novel recursive approach is proposed under certain conditions the approach applies to noncausal models

a new c1 finite element full heptic a new c1 finite element complete in 7th degree polynomial basis is described and compared with other c1 elements in an eigen elements analysis

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

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

a new triangular and tetrahedral basis for high order hp finite element methods in this paper we describe the foundations of a new hierarchical modal basis suitable for high order hp finite element discretizations on unstructured meshes it is based on a generalized tensor product of mixed weight jacobi polynomials the generalized tensor product property leads to a low operation count with the use of sum factorization techniques variable p order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two and three dmensional computational domains employing standard meshes

approaches of fir system identification with noisy data using higher order statistics the problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is discussed the system is driven by an independently identically distributed nongaussian sequence that is not observed the noise is additive and may be colored and nongaussian following some existing linear parametric approaches to this problem a linear method and a modification to an existing linear method are proposed for consistent parameter estimation in measurement noise under the assumption that the system order is known both recursive closed form and batch least squares versions of the parameter estimators are presented the existing and the proposed linear methods utilize only a partial set of the relevant output statistics this restriction being necessary to obtain a linear estimator whereas there exist nonlinear method that exploit a much larger set of output statistics a simulation example where two existing linear methods and the two new methods are compared to two existing nonlinear methods is presented

on the application of two gauss legendre quadrature rules for composite numerical integration over a tetrahedral region in this paper we first present a gauss legendre quadrature rule for the evaluation of i f f t ff x y z dxdydz where f x y z is an analytic function in x y z and tis the standard tetrahedral region x y z 0 x y z i x y z 1 in three space x y z we then use a transformation x x y y and z z to change the integral into an equivalent integral i 1 1 1 1 1 1 f x y x y z d d d over the standard 2 cube 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 then a second gauss legendre quadrature rule of composite type is obtained this rule is derived by discretising the tetrahedral region t into four new tetrahedra t c i i 1 2 3 4 of equal size which are obtained by joining the centroid of t c 1 4 1 4 1 4 to the four vertices of t by use of the affine transformations defined over each t c i and the linearity property of integrals leads to the result i 4 i 1 tci f x y z dxdydz 1 4 t g x y z dxdydz where g x y z 1 p 3 f x k x y z y k x y z z k x y z x k x k x y z y k y k x y z and z k z k x y z refer to an affine transformations which map each t c i into the standard tetrahedral region t we then write i t g x y z dxdydz 1 0 1 0 1 0 g x y z x y z d d d and a composite rule of integration is thus obtained we next propose the discretisation of the standard tetrahedral region t into p 3 tetrahedra t i i 1 1 p 3 each of which has volume equal to 1 6p 3 units we have again shown that the use of affine transformations over each t and the use of linearity property of integrals leads to the result t f x y z dxdydz p3 i 1 t c i f x y z dxdydz p3 1 t p f x p y p z p dx p dy p dz p 1 p3 t h x y z dxdydz where p3 h x y z 1 f x p x y z y p x y z z p x y z x p x p x y z y p y p x y z and z p z p x y z refer to the affine transformations which map each t i in x p y p z p space into a standard tetrahedron t in the x y z space we can now apply the two rules earlier derived to the integral t h x y z dxdydz this amounts to the application of composite numerical integration of t into p3 and 4p3 tetrahedra of equal sizes we have demonstrated this aspect by applying the above composite integration method to some typical triple integrals

optimal partial regularity for nonlinear sub elliptic systems ncetxmu national natural science foundation of china nsaf nsf of china 10976026 natural science foundation of zhejiang province y6110078

an iterative algorithm for polynomial approximation of rational triangular bezier surfaces this paper presents the weighted progressive iteration approximation wpia property for the triangular bernstein basis over a triangle domain with uniform parameters which is extended from the pia property for triangular bernstein basis proposed by chen and wang in j chen g j wang progressive iterative approximation for triangular bezier surfaces computer aided design 43 2011 889 895 we also provide how to choose an optimal value of the weight to own the fastest convergence rate for triangular bernstein basis furthermore a new and efficient iterative method is proposed for polynomial approximation of rational triangular bezier surfaces the algorithm is reiterated until a halting condition about approximation error is satisfied and the approximation error in l p norm p 1 2 is calculated by the symmetric gauss legendre quadrature rule for composite numerical integration over a triangular surface finally several numerical examples are presented to validate the effectiveness of this method

performance analysis of estimation algorithms of nonstationary arma processes the correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive ar moving average ma and arma systems by using estimation residuals in place of unmeasurable noise terms in information vector or matrix we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity ergodicity or existence of higher order moments furthermore we derive the conditions for convergence of the parameter estimation the simulation results validate the convergence theorems proposed

a convergence analysis of an h version finite element method with high order elements for two dimensional elasto plasticity problems in this paper we will give an h version finite element method for a two dimensional nonlinear elasto plasticity problem a family of admissible constitutive laws based on the so called gauge function method is introduced first and then a high order h version semidiscretization scheme is presented the existence and uniqueness of the solution for the semidiscrete problem are guaranteed by using some special properties of the constitutive law and finally we will show that as the maximum element size h longrightarrow 0 the solution of the semidiscrete problem will converge to the solution of the continuous problem the high order h version discretization scheme introduced here is unusual if the partition of the spatial space only has rectangles or parallelograms involved then there would not be any limit on the element degree however if the partition of the spatial space has some triangular elements then only certain combinations of finite element spaces for displacement and stress functions can be used the discretization scheme also provides a useful idea for applications of hp version or high order h version finite element methods for two dimensional problems where the elasto plastic body is not a polygon such as a disk or an annulus

singularity subtraction technique for high order polynomial vector basis functions on planar triangles in this paper a singularity subtraction technique is developed for computing the impedance matrix elements of various electromagnetic surface integral equation formulations with the galerkin method and high order basis functions analytical closed form formulas for computing surface integrals with r r sup n n spl ges 3 singularities times polynomial nodal shape functions of arbitrary order on a planar triangle are presented

second order accurate derivatives and integration schemes for meshfree methods summary the consistency condition for the nodal derivatives in traditional meshfree galerkin methods is only the differentiation of the approximation consistency dac one missing part is the consistency between a nodal shape function and its derivatives in terms of the divergence theorem in numerical forms in this paper a consistency framework for the meshfree nodal derivatives including the dac and the discrete divergence consistency ddc is proposed the summation of the linear ddc over the whole computational domain leads to the so called integration constraint in the literature a three point integration scheme using background triangle elements is developed in which the corrected derivatives are computed by the satisfaction of the quadratic ddc we prove that such smoothed derivatives also meet the quadratic dac and therefore the proposed scheme possesses the quadratic consistency that leads to its name qc3 numerical results show that qc3 is the only method that can pass both the linear and the quadratic patch tests and achieves the best performances for all the four examples in terms of stability convergence accuracy and efficiency among all the tested methods particularly it shows a huge improvement for the existing linearly consistent one point integration method in some examples copyright 2012 john wiley sons ltd

closed form recursive estimation of ma coefficients using autocorrelations and third order cumulants the authors derive a simple recursive closed form algorithm for estimating the parameters of a moving average ma model of known order using only the autocorrelation and the 1 d diagonal slice of the third order cumulant of its response to excitation by an unobservable non gaussian iid process the output may be corrupted by zero mean nonskewed white noise of unknown variance the autoregressive moving average arma case is briefly discussed

mixed inner outer iteration technique based surface integral equations for fast solving em scattering from penetrable objects in this paper a mixed inner outer iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures the most important novelty of the proposed technique is combining the tangential poggio miller chang harrington wu tsai as outer iteration and the electric magnetic current combined field integral equation as inner iteration respectively in this case the new method offers the guarantee of high accuracy with faster convergence especially for electrically dielectric structures in large scale furthermore it presents an excellent compatibility with sparse approximate inverse preconditioning numerical results are given to demonstrate the accuracy efficiency and compatibility of the proposed method

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

numerical integrations over an arbitrary quadrilateral region in this paper double integrals over an arbitrary quadrilateral are evaluated exploiting finite element method the physical region is transformed into a standard quadrilateral finite element using the basis functions in local space then the standard quadrilateral is subdivided into two triangles and each triangle is further discretized into 4xn 2 right isosceles triangles with area 12n 2 and thus composite numerical integration is employed in addition the affine transformation over each discretized triangle and the use of linearity property of integrals are applied finally each isosceles triangle is transformed into a 2 square finite element to compute new n 2 extended symmetric gauss points and corresponding weight coefficients where n is the lower order conventional gauss legendre quadratures these new gauss points and weights are used to compute the double integral examples are considered over an arbitrary domain and rational and irrational integrals which can not be evaluated analytically

information transfer between incompatible finite element meshes application to coupled thermo viscoelasticity this article is concerned with information transfer between non matching finite element meshes such a feature is not new in the literature but we focus herein on a geometric approach to transfer solution fields in order to be as application independent as possible moreover the dedicated case concerns the transfer of finite element fields defined at integration points of the meshes and allows iterative exchange of fields in both directions to do so we propose an extension to the mortar technique that fulfills these goals and that does not suffer from a high computational cost the application is the simulation of a strongly coupled thermo viscoelastic problem with phase transition solved with a partitioning technique

optimal partial regularity for weak solutions of nonlinear sub elliptic systems in carnot groups abstract this paper is concerned with partial regularity for weak solutions to nonlinear sub elliptic systems in divergence form in carnot groups the technique of a harmonic approximation introduced by simon and developed by duzaar and grotowski is adapted to our context we establish caccioppoli type inequalities and partial regularity with optimal local holder exponents for horizontal gradients of weak solutions to systems under super quadratic natural structure conditions and super quadratic controllable structure conditions respectively

numerical approximation of internal discontinuity interface problems this work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain the interface is characterized via a level set function the discontinuities are accounted for by using suitable extension operators whose numerical implementation requires a very low computational effort after carrying out the error analysis numerical results to validate our approach are presented in one two and three dimensions

general behavior and shear center location of prismatic anisotropic beams via power series abstract the behavior of a tip loaded anisotropic cantilever beam with an arbitrary cross section is studied using saint venant s semi inverse method along with a power series solution for the local in plane and out of plane deformation warping functions the power series coefficients are determined by solving a set of variationally derived linear algebraic equations using the resulting three dimensional displacement solutions the shear deformation associated with applied tip loads is investigated as well as the shear center location two different definitions of the shear center are presented for anisotropic beams by extending existing approaches developed for isotropic sections both of the extended definitions reveal the linear dependency of the shear center location on beam length numerical results are presented for three different cross sections ellipse triangle naca 0012 airfoil and two different materials al 6061 t6 off angle high strength graphite epoxy fibers

on structural shape optimization using an embedding domain discretization technique summary this contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique the evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization we consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements exterior elements and elements intersected by the physical domain boundary a selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component thereby we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration as it is the case for a standard lagrangian approach to structural shape optimization still we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process in order to avoid irregular and impracticable design updates we consider a geometric regularization technique to render feasible descent directions for the course of the optimization this article is protected by copyright all rights reserved

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

fast matlab assembly of fem matrices in 2d and 3d we propose an effective and flexible way to assemble finite element stiffness and mass matrices in matlab we apply this for problems discretized by edge finite elements typical edge finite elements are raviart thomas elements used in discretizations of h div spaces and nedelec elements in discretizations of h curl spaces we explain vectorization ideas and comment on a freely available matlab code which is fast and scalable with respect to time

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

fir system identification using higher order statistics alone this paper focuses on fir system identification in gaussian arma noise using higher order cumulants alone two new types of cumulant based normal equations are established and two algorithms are proposed for ma parameter estimation simulations verify the high performance of the new developments

singular value decomposition based ma order determination of non gaussian arma models singular value decomposition svd based moving average ma order determination of non gaussian processes using higher order statistics is addressed it is shown that the ma order determination of autoregressive moving average arma models is equivalent to the rank determination of a certain error matrix and a svd approach is proposed its simplified form is applied to pure ma models to improve the robustness of the order selection a combination of the svd and the product of diagonal entries pode test is proposed some interesting applications of the two svd approaches are presented and simulations verify their performance

edged based smoothed point interpolation method for acoustic radiation with perfectly matched layer abstract it is known that for exterior acoustics the domain based finite element method always encounters the accuracy loss for high wavenumbers and the difficulty in dealing with the sommerfeld radiation condition in this work by using the polynomial and radial bases with specific node selection schemes the point interpolation method with the generalized gradient smoothing technique is employed to improve the accuracy for acoustic computations the appropriately softened acoustical stiffness of the discrete model is constructed based on the edge based smoothing domains via the gradient smoothing technique in addition the perfectly matched layer technique enables the smoothed point interpolation method to investigate exterior acoustics the complex coordinate transformation is utilized to determine the proper parameters for the perfectly matched layer through theoretical and numerical analyses several typical acoustic problems are analyzed revealing that better accuracy is obtained by the present method compared with the finite element method especially for high wavenumbers

on numerical integration in isogeometric subdivision methods for pdes on surfaces abstract subdivision surfaces offer great flexibility in capturing irregular topologies combined with higher order smoothness for instance loop and catmull clark subdivision schemes provide c 2 smoothness everywhere except at extraordinary vertices where the generated surfaces are c 1 smooth the combination of flexibility and smoothness leads to their frequent use in geometric modeling and makes them an ideal candidate for performing isogeometric analysis of higher order problems with irregular topologies e g thin shell problems in the neighborhood of extraordinary vertices however the resulting surfaces and the functions defined on them are non polynomial thus numerical integration based on quadrature has to be performed carefully to preserve the expected higher order consistency this paper presents a detailed case study of different quadrature schemes for isogeometric discretizations of partial differential equations on closed surfaces with loop s subdivision scheme as model problems we consider elliptic equations with the laplace beltrami and the surface bi laplacian operator as well as the associated eigenvalue problem for the laplace beltrami operator a particular emphasis is on the robustness of the approach in the vicinity of extraordinary vertices based on a series of numerical experiments different quadrature schemes are compared mid edge quadrature which can easily be implemented via a lookup table turns out to be a preferable choice due to its robustness and efficiency

machine precision evaluation of singular and nearly singular potential integrals by use of gauss quadrature formulas for rational functions a new technique for machine precision evaluation of singular and nearly singular potential integrals with 1 r singularities is presented the numerical quadrature scheme is based on a new rational expression for the integrands obtained by a cancellation procedure in particular by using library routines for gauss quadrature of rational functions readily available in the literature this new expression permits the exact numerical integration of singular static potentials associated with polynomial source distributions the rules to achieve the desired numerical accuracy for singular and nearly singular static and dynamic potential integrals are presented and discussed and several numerical examples are provided

adjoint based h p adaptive discontinuous galerkin methods for the 2d compressible euler equations in this paper we investigate and present an adaptive discontinuous galerkin algorithm driven by an adjoint based error estimation technique for the inviscid compressible euler equations this approach requires the numerical approximations for the flow i e primal problem and the adjoint i e dual problem which corresponds to a particular simulation objective output of interest the convergence of these two problems is accelerated by an hp multigrid solver which makes use of an element gauss seidel smoother on each level of the multigrid sequence the error estimation of the output functional results in a spatial error distribution which is used to drive an adaptive refinement strategy which may include local mesh subdivision h refinement local modification of discretization orders p enrichment and the combination of both approaches known as hp refinement the selection between h and p refinement in the hp adaptation approach is made based on a smoothness indicator applied to the most recently available flow solution values numerical results for the inviscid compressible flow over an idealized four element airfoil geometry demonstrate that both pure h refinement and pure p enrichment algorithms achieve equivalent error reductions at each adaptation cycle compared to a uniform refinement approach but requiring fewer degrees of freedom the proposed hp adaptive refinement strategy is capable of obtaining exponential error convergence in terms of degrees of freedom and results in significant savings in computational cost a high speed flow test case is used to demonstrate the ability of the hp refinement approach for capturing strong shocks or discontinuities while improving functional accuracy