spatiotemporal complexity of the cubic quintic nonlinear schrodinger equation the integrability of the cubic quintic nonlinear schrodinger equation is investigated numerically by analytically studying the linear stability of the homogeneous state and numerically solving such a continuum hamiltonian dynamic system the authors show that the quintic nonlinear term leads to a spatiotemporal complexity of wave fields and illustrate that this behaviour is associated with the stochastic partition of energy in fourier modes in addition they show the presence of the stochastic motion is due to the homoclinic orbit crossings

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

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

geometry of the modulational instability iii homoclinic orbits for the periodic sine gordon equation in this paper the homoclinic geometric structure of the integrable sine gordon equation under periodic boundary conditions is developed specifically focus is given to orbits homoclinic to n tori simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given a labeling is provided which identifies and catalogues all such orbits these orbits are related in a one to one manner to linearized instabilities explicit formulas for all homoclinic orbits are given in terms of backlund transformations

economical symmetrical quadrature rules for complete polynomials over a square domain it is of interest in numerical analysis to develop symmetrical quadrature rules for integration of complete polynomial functions over a square domain with minimum computational effort gaussian product quadrature rules integrate such functions with maximum effort symmetrical quadrature rules are developed and presented for integration of complete polynomial functions up to 21st order with minimum computational effort

periodic and chaotic behaviour in a reduction of the perturbed korteweg de vries equation the dynamical behaviour of a reduction of the forced and damped korteweg de vries equation is studied numerically chaos arising from subharmonic instability and homoclinic crossings are observed both period doubling bifurcations and the melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour here characterised by a positive lyapunov exponent supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits and their behaviour under perturbation using melnikov functions

homoclinic crossings and pattern selection the correlations between a homoclinic orbit hmo and coherent patterns in the nonlinear schr odinger model are discussed in a hamiltonian situation two independent patterns are revealed to exist one corresponds to a motion within an hmo and the other outside of an hmo the study further illustrates when the hamiltonian constraint is released the significance of an hmo on the patterns dynamics by presenting the irregular hmo crossings and the resulting chaotic selections between the patterns

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

integration of singular enrichment functions in the generalized extended finite element method for three dimensional problems a mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized extended finite element method the integration scheme is applicable to 2d and 3d problems including arbitrarily shaped triangles and tetrahedra implementation of the proposed scheme in existing codes is straightforward numerical examples for 2d and 3d problems demonstrate the accuracy and convergence properties of the technique copyright 2008 john wiley sons ltd

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

application of group representation theory to derive hermite interpolation polynomials on a triangle current methods used to devise sets of hermite interpolation polynomials of minimal order that ensure c n continuity across triangular element boundaries in two dimensions are not readily extensible to higher dimensions the extension of such methods is especially difficult when the number of degrees of freedom afforded by data at points is different from the number of degrees of freedom determined by the coefficients of a complete polynomial basis to a particular order this work introduces a formalism based on group representation theory that can accomplish this task in general the method is introduced through the derivation of c 1 continuous hermite polynomials that interpolate data at the three vertices of an equilateral triangular element these interpolation polynomials are reported here for the first time the polynomials derived here are compared to the standard polynomials defined in a right triangle by using the two sets of polynomials to solve the laplace equation over finite elements the methodology presented here is of use in higher dimensional elements when the complete polynomial degrees of freedom exceed the total c n degrees of freedom at the nodes

the numerical evaluation of hadamard finite part integrals a quadrature rule is described for the numerical evaluation of hadamard finite part integrals with a double pole singularity within the range of integration the rule is based upon the observation that such an integral is the derivative of a cauchy principal value integral

dynamic properties of cubic nonlinear schrodinger equation with varying nonlinear parameter the dynamic properties of the cubic nonlinear schrodinger equation are investigated numerically using the symplectic scheme euler centred scheme we discuss the dynamic behaviour of the cubic nonlinear schrodinger equation with varying nonlinear parameter the results show that the system exhibits regular recurrence for weakly nonlinearity we also illustrate that the system will exhibit varying dynamic behaviour with increasing nonlinear parameter i e the system will show the homoclinic orbit hmo crossing quasi recurrence pseudorecurrence irregular motion or stochastic motion for a strongly nonlinear constants

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

entropy stable shock capturing space time discontinuous galerkin schemes for systems of conservation laws we present a streamline diffusion shock capturing spacetime discontinuous galerkin dg method to approximate nonlinear systems of conservation laws in several space dimensions the degrees of freedom are in terms of the entropy variables and the numerical flux functions are the entropy stable finite volume fluxes we show entropy stability of the formally arbitrarily high order accurate method for a general system of conservation laws furthermore we prove that the approximate solutions converge to the entropy measure valued solutions for nonlinear systems of conservation laws convergence to entropy solutions for scalar conservation laws and for linear symmetrizable systems is also shown numerical experiments are presented to illustrate the robustness of the proposed schemes

novel cloning machine with supplementary information probabilistic cloning was first proposed by duan and guo then pati established a novel cloning machine ncm for copying superposition of multiple clones simultaneously in this paper we deal with the novel cloning machine with supplementary information ncmsi for the case of cloning two states we demonstrate that the optimal efficiency of the ncmsi in which the original party and the supplementary party can perform quantum communication equals that achieved by a two step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties from this equivalence it follows that ncmsi may increase the success probabilities for copying also an upper bound on the unambiguous discrimination of two nonorthogonal pure product states is derived our investigation generalizes and completes the results in the literature

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

periodic and chaotic behaviour in a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations abstract the dynamical behaviour of a reduced form of the perturbed generalized korteweg de vries and kadomtsev petviashvili equations extension of the korteweg de vries equation to two space variables are studied in this paper harmonic solutions of non resonance and primary resonance are obtained using the perturbation method chaotic motion under harmonic excitations is studied using the melnikov method a wide range of solutions for the reduced perturbed generalized korteweg de vries equations in which non linear phenomena appearing within transition from regular harmonic response periodic solutions to chaotic motion are obtained using the time integration runge kutta method when chaos is found it is detected by examining the phase plane the poincare map the sensitivity solution of the solution to initial conditions and by calculating the largest lyapunov exponent

efficient symmetrical cubature rules for complete polynomials of high degree over the unit cube the fully symmetrical cubature rules developed and presented are at present the most economically available for numerical integration over the unit cube of complete polynomial functions up to and including nineteenth order conventional gaussian triple product integration formulae by comparison require more than twice as many integration points and weights

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

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

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

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

direct computation of cauchy principal value integrals in advanced boundary elements this paper presents a new method for the direct computation of strongly singular integrals existing in the cauchy principal value sense it can be usefully applied in the solution by the direct boundary element method of many different problems initially some considerations are provided in order to summarize the state of the art on this issue then the features of the proposed method are reported the procedure allows the direct calculation of cauchy principal value integrals with first order singularity and it is applicable even in advanced boundary element methods employing high order elements it requires only the use of standard gaussian quadrature formulae plus the computation of a logarithmic term some examples show the effectiveness and efficiency of the procedure

remarks on the gauss quadrature rule for a particular class of finite part integrals the method of finite part hadamard type or hypersingular integrals is already a standard approach in applied numerical methods in engineering and mainly in acoustics fluid dynamics elasticity and fracture mechanics here we study the convergence of the non classical possessing a negative node outside the integration interval as well as a negative weight corresponding to this node gauss legendre quadrature rule for finite part integrals on the interval 0 1 with the weight function 1 y and we prove its validity for integrands possessing a continuous first derivative the case of integrands possessing a higher order derivative is also considered and the rate of convergence is established these results are based on the derivation of a bound for the negative node in the above quadrature rule and further on the theory of convergence of the classical gauss quadrature rule numerical results verifying the results of this paper are also displayed the present results can be generalized to the gauss laguerre similarly non classical quadrature rule for finite part integrals on the interval 0 as well as to the two special but important in engineering applications non classical gaussian quadrature rules for cauchy type principal value integrals and mangler type finite part integrals have been proposed by tsamasphyros and dimou

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

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

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

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

dynamical survey of the dual power zakharov kuznetsov burgers equation with external periodic perturbation abstract we investigate the dynamical behavior of the newly introduced dual power zakharov kuznetsov burgers equation using bifurcation theory of planar dynamical systems we study bifurcations of traveling wave solutions of the dual power zakharov kuznetsov burgers equation in presence and absence of viscosity effect in presence of an external periodic perturbation we discuss the periodic and chaotic motions of the perturbed dual power zakharov kuznetsov burgers equation by analyzing phase projection analysis time series analysis poincare section and sensitivity analysis the effect of viscosity plays an important role in the transition from chaotic motion to periodic motion of the perturbed dual power zakharov kuznetsov burgers equation

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

derivation of a new analytical solution for a general two dimensional finite part integral applicable in fracture mechanics an exact expression is derived for the general finite part integral over an inclined ellipticaldomain r denotes the distance of a point in to the singular point is a general function of the cartesian co ordinates x0 y0 the boundary of the region represents the equation z x0 y0 o these integrals appear during the numerical solution of plane crack problems in three dimensional elasticity where they are the dominant part of a hypersingular integral equation the availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and simultaneously lead to quicker numerical results the considered finite part integral can be expressed in closed form as function of complete elliptical integrals or gauss hypergeometric functions respectively formuias for special cases and some i j values and their numerical verification are given in appendices ii and iii

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

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

numerical solution of three dimensional crack problem by using hypersingular integral equation in this paper a flat crack with the normal boundary loading on the crack face is embedded in an infinite medium the relevant problem is called the three dimensional crack problem hereafter the hypersingular integral equation is used to solve the mentioned problem two innovative points are suggested in this paper a the involved hypersingular integrals are evaluated in a polar coordinate system and are converted to the repeated integrals b one of the repeated integral is hypersingular and the involved integrated function is approximated by a product of the weight function and chebyshev polynomials the hypersingular integrals can be evaluated numerically by using a known result therefore the hypersingular integral equation for the three dimensional crack problem can be solved immediately finally numerical examples are given to demonstrate the efficiency of the suggested approach

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

dynamic behaviors and soliton solutions of the modified zakharov kuznetsov equation in the electrical transmission line the modified zakharov kuznetsov mzk equation in the electrical transmission line is investigated in this paper different expressions on the parameters in the mzk equation are given by means of the hirota method bilinear forms and soliton solutions of the mzk equation are obtained linear stability analysis yields the instability condition for such soliton solutions we find that the soliton amplitude becomes larger when the inductance l and capacitance c 0 decrease phase plane analysis is conducted on the mzk equation for the properties at equilibrium points then we investigate the perturbed mzk equation which can be proposed when the external periodic force is considered both the weak and developed chaotic motions are observed our results indicate that the two chaotic motions can be manipulated with certain relation between the absolute values of nonlinear terms and the perturbed one we also find that the chaotic motions can be weakened with the absolute values of l and c 0 decreased

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

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

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

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

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

a high order locally corrected nystrom scheme for charge current integral equations a high order nystrom scheme is developed for electromagnetic em scattering problems of smooth objects the implementation is based on different well known charge current formulations this study aims to develop a novel quadrature scheme to compute different singular integrals that appear on integral equation methods in ems the proposed quadrature scheme is used on a locally corrected nystrom method and applied to charge current integral equations to obtain a fast accurate and a low frequency stable method to solve em scattering problems the proposed method allows obtaining accuracy in the range 4 10 digits in the near electric and magnetic scattered field for certain simple geometries and a wide range of frequencies we also do a preliminary research on nonsmooth geometries obtaining a certain degree of accuracy depending on the particular charge current integral equation used

gauss quadrature rules for finite part integrals we construct a set of polynomials n x which are orthogonal with respect to w x x 2 where wx is a weight function these polynomials can be used for the definition of a gauss quadrature formula for the finite part integral the process is exactly the same as the one used for the extraction of the classical gauss formula for the riemann integrals three different methods are derived the first and most accurate quadrature formula is successfully tested in some numerical examples the proposed quadrature formulas have many applications in problems of mathematical physics mechanics etc

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

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

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

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

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

on the adaptive coupling of fem and bem in 2 d elasticity this paper concerns the combination of the finite element method fem and the boundary element method bem using the symmetric coupling as a model problem in two dimensions we consider the hencky material a certain nonlinear elastic material in a bounded domain with navier lame differential equation in the unbounded complementary domain using some boundary integral operators the problem is rewritten such that the galerkin procedure leads to a fem bem coupling and quasi optimally convergent discrete solutions beside this a priori information we derive an a posteriori error estimate which allows up to a constant factor the error control in the energy norm since information about the singularities of the solution is not available a priori in many situation and having in mind the goal of an automatic mesh refinement we state adaptive algorithms for the h version of the fem bem coupling illustrating numerical results are included

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

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

finite element solution of a boundary integral equation for mode i embedded three dimensional fractures the singular integral equation governing the opening of a mode i embedded three dimensional fracture in an infinite solid was solved by applying the finite element method the strategy is to formulate the equation into weak form and to transfer the differentiation from the singular term 1 r in the equation to the test function a numerical algorithm was thus developed the numerical solutions for circular and elliptical fractures under the action of polynomial pressure distributions were compared with the analytical solutions by green and sneddon 12 irwin 13 shah and kobayashi14 and nishioka and atluri 16 the results have demonstrated that the numerical method reported is accurate and efficient

dynamics of the generalized kp mew burgers equation with external periodic perturbation the generalized kadomtsevpetviashvili modified equal width burgers kp mew burgers equation is introduced for the first time the qualitative change of the traveling wave solutions of the kp mew burgers equation is studied using numerical simulations considering an external periodic perturbation the periodic and chaotic motions of the perturbed kp mew burgers equation are investigated by using the phase projection analysis time series analysis poincare section and bifurcation diagram the parameter a nonlinear coefficient plays a crucial role in the periodic motions and chaotic motions through period doubling route to chaos of the perturbed kp mew burgers equation

chaotic transport and integrable instabilities in a near integrable many particle hamiltonian lattice abstract this paper is a report of detailed numerical experiments on a large dimensional hamiltonian lattice which arises as a nearly integrable discretization of the periodic sine gordon equation through four different one parameter families of initial data we focus on the interplay between numerically observable near integrable behavior quantified by modern statistical diagnostics and the integrable pde solutions and phase space geometry associated with the initial data transitions are observed within each family from quasiperiodic behavior to chaotic motion which is sometimes accompanied by transport toward equipartition these transitions in the near integrable system are correlated with integrable features of the initial data in particular transitions from neutrally stable to exponentially unstable sine gordon solutions and associated homoclinic orbits geometrically these correspond to transitions from neutrally stable tori to whiskered tori our results indicate that 1 positive lyapunov exponents our messure of chaos in near integrable orbits coincide one to one with integrable pde instabilities and homoclinic orbits 2 the statistical transition to equipartition of energy on a long fixed timescale occurs only if but not necessarily if there are integrable instabilities and associated whiskered tori the rate of transport appears to depend on the amplitude of the homoclinic degrees of freedom 3 isolated cases of discreteness induced instabilities and action transport are observed these return to quasiperiodic flow at finer discretizations 4 a simple measure such as energy of the initial data is not an accurate predictor of chaotic or recurrent behavior one family of initial data exhibits as the energy increases alternating windows of quasiperiodic and chaotic orbits

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

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

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

distribution of the discretization and algebraic error in numerical solution of partial differential equations abstract in the adaptive numerical solution of partial differential equations local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain since the discretized algebraic problems are not solved exactly a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error the main goal of this paper is to illustrate using standard boundary value model problems that this may not hold on the contrary the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain the illustrated phenomenon is of general significance and it is not restricted to some particular problems or dimensions to our knowledge the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere

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

probabilistic broadcasting of mixed states it is well known that the non broadcasting theorem proved by barnum et al is a fundamental principle of quantum communication as we are aware optimal broadcasting ob is the only method to broadcast noncommuting mixed states approximately in this paper motivated by the probabilistic cloning of quantum states proposed by duan and guo we propose a new way for broadcasting noncommuting mixed states probabilistic broadcasting pb and we present a sufficient condition for pb of mixed states to a certain extent we generalize the probabilistic cloning theorem from pure states to mixed states and in particular we generalize the non broadcasting theorem since the case that commuting mixed states can be exactly broadcast can be thought of as a special instance of pb where the success ratio is 1 moreover we discuss probabilistic local broadcasting plb of separable bipartite states

a bi cubic transformation for the numerical evaluation of the cauchy principal value integrals in boundary methods the numerical strategies employed in the evaluation of singular integrals existing in the cauchy principal value cpv sense are undoubtedly one of the key aspects which remarkably affect the performance and accuracy of the boundary element method bem thus a new procedure based upon a bi cubic co ordinate transformation and oriented towards the numerical evaluation of both the cpv integrals and some others which contain different types of singularity is developed both the ideas and some details involved in the proposed formulae are presented obtaining rather simple and attractive expressions for the numerical quadrature which are also easily embodied into existing bem codes some illustrative examples which assess the stability and accuracy of the new formulae are included