a nodal integration and post processing technique based on voronoi diagram for galerkin meshless methods a stabilized nodal integration technique is adopted by adding the square of the residual of the equilibrium equation to the potential energy functional an approach is proposed based on voronoi diagram to evaluate nodal volumes accurately it is a key issue for nodal integration of galerkin meshless methods furthermore as the dual of voronoi diagram the corresponding delaunay triangles are at hand provided voronoi diagram construction is completed a realistic technique is proposed based on background delaunay triangles for post processing of meshless results in the whole domain of interest two elastic stress analysis problems are investigated which demonstrate the approach is realistic versatile and robust

radial spline collocation method for static analysis of beams conventional spline collocation method scm uses equally spaced knots in the computation of approximation however when load distribution geometry material property of structure are discontinuous it will greatly reduce accuracy the goal of this paper is mainly to develop unequally spaced knots to improve the disadvantage of using equally spaced knots applying the concept of radial basis functions rbf the spline function is transformed into radial spline function rsf consequently rsf can conveniently calculate the values for unequally spaced knots so that the complicated beam problems with discontinuous characteristics can be solved accurately and efficiently by the proposed radial spline collocation method rscm in this paper the proposed rscm also can be extended to solve other structural problems such as frame plate shell etc

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

numerical solution to the unsteady two dimensional schrodinger equation using meshless local boundary integral equation method a meshless local boundary integral equation lbie method is proposed to solve the unsteady two dimensional schrodinger equation the method is based on the lbie with moving least squares mls approximation for the mls approximation nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables a time stepping method is employed to deal with the time derivative an efficient method for dealing with singular domain integrations that appear in the discretized equations is presented finally numerical results are considered for some examples to demonstrate the accuracy efficiency and high rate of convergence of this method copyright 2008 john wiley sons ltd

on distortion compensated dither modulation data hiding with repetition coding an exhaustive analysis of the distortion compensated dither modulation dc dm data hiding method with repetition coding is presented two decoding strategies maximum likelihood lattice decoding and euclidean distance decoding are discussed and some simplifications presented an exact performance analysis in terms of the bit error rate ber is given such an exact analysis is currently not available in the literature two methods for computing the exact ber and several approximations and bounds most of them in closed form are provided these approximations are employed to propose two novel improvements on the standard dc dm method with repetition the use of a weighted euclidean distance with optimizable weights and a vector form of the distortion compensation parameter both account for significant performance improvements dc dm is compared with quantization methods in the projected domain showing worse performance against additive noise attacks but higher robustness to cropping attacks a performance analysis of dc dm under coarse quantization that can be specialized to jpeg compression is also supplied all our results are validated with numerical simulations with both synthetic data and real images

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a parallel algorithm for the computation of invariant tori in large scale dissipative systems a parallelizable algorithm to compute invariant tori of high dimensional dissipative systems obtained upon discretization of pdes is presented the size of the set of equations to be solved is only a small multiple of the dimension of the original system the sequential and parallel implementations are compared with a previous method sanchez et al 2010 11 showing that important savings in wall clock time can be achieved in order to test it a thermal convection problem of a binary mixture of fluids has been used the new method can also be applied to problems with very low rotation numbers for which the previous is not suitable this is tested in two examples of two dimensional maps

on the convergence analysis stability and implementation of meshless local radial point interpolation on a class of three dimensional wave equations summary in this article the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt ut u uxx uyy uzz f x y z t xt x y z rd d 2 3 t 0 subject to given initial and dirichlet boundary conditions the main difficulty of the great number of methods in full 3 d problems is the large computational costs in meshless local radial point interpolation method it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions the point interpolation method with the help of radial basis functions is proposed to construct shape functions that have kronecker delta function property a weak formulation with the heaviside step function converts the set of governing equations into local integral equations on local subdomains a two step time discretization method is employed to evaluate the time derivatives this suggests crank nicolson technique to be applied on the right hand side of the equation the convergence analysis and stability of the method are fully discussed three illustrative examples are presented and satisfactory agreements are achieved it is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones copyright 2015 john wiley sons ltd

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

implementation of meshless lbie method to the 2d non linear sg problem in this paper the meshless local boundary integral equation lbie method for numerically solving the non linear two dimensional sine gordon sg equation is developed the method is based on the lbie with moving least squares mls approximation for the mls nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables the approximation functions are constructed entirely using a set of scattered nodes and no element or connectivity of the nodes is needed for either the interpolation or the integration purposes a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of method to deal with the unsteady non linear problems in large domains copyright 2009 john wiley sons ltd

the natural neighbour petrov galerkin method for elasto statics in this paper an efficient and accurate meshless natural neighbour petrov galerkin method nnpg is proposed to solve elasto static problems in two dimensional space this method is derived from the generalized meshless local petrov galerkin method mlpg as a special case in the nnpg the local supported trial functions are constructed based on the non sibsonian interpolation and test functions are taken as the three node triangular fem shape functions the local weak forms of the equilibrium equation and the boundary conditions are satisfied in local polygonal sub domains these sub domains are constructed with delaunay tessellations and domain integrals are evaluated over included delaunay triangles by using gaussian quadrature scheme as this method combines the advantages of natural neighbour interpolation with petrov galerkin method together no stiffness matrix assembly is required and no special treatment is needed to impose the essential boundary conditions several numerical examples are presented and the results show the presented method is easy to implement and very accurate for these problems copyright 2005 john wiley sons ltd

computation continuation and bifurcation of torus solutions for dissipative maps and ordinary differential equations abstract a periodic solution can be considered as a fixed point of a poincare map we shall demonstrate how we can generalize this fixed point equivalence to quasi periodic solutions with two periods thus the quasi periodic solution or bi periodic solution will be a fixed point of a more general poincare map the stability of the bi periodic solution is then equivalent to the stability of the fixed point we demonstrate how we can follow the fixed point in dependence of any control parameter in the system furthermore we demonstrate both how the bi periodic solution may bifurcate to more complicated solutions and how it may arise as a bifurcation from a periodic solution our work is algorithmic in spirit and our statements are based on numerical evidence

performance analysis of existing and new methods for data hiding with known host information in additive channels a considerable amount of attention has been paid lately to a number of data hiding methods based in quantization seeking to achieve in practice the results predicted by costa 1983 for a channel with side information at the encoder with the objective of filling a gap in the literature this paper supplies a fair comparison between significant representatives of both this family of methods and the former spread spectrum approaches that make use of near optimal ml decoding the comparison is based on measuring their probabilities of decoding error in the presence of channel distortions accurate analytical expressions and tight bounds for the probability of decoding error are given and validated by means of monte carlo simulations for dithered modulation dm a novel technique that allows us to obtain tighter bounds to the probability of error is presented within the new framework the strong points and weaknesses of both methods are distinctly displayed this comparative study allows us to propose a new technique named quantized projection qp which by adequately combining elements of those previous approaches produces gains in performance

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

on the reducibility of linear differential equations with quasiperiodic coefficients the system x a eq t x in rd is considered where a is a constant matrix and q a quasiperiodic analytic matrix with r basic frequencies the eigenvalues of a are arbitrary including the purely imaginary case suppose that the set formed by the eigenvalues of a and the basic frequencies of q satisfies a nonresonant condition then there is a positive measure cantorian set e such that for e e the system is reducible to constant coefficients by means of a quasiperiodic change of variables provided a nondegeneracy condition holds this condition prevents locking at resonance

performance analysis of st dm watermarking in presence of nonadditive attacks the performance of spread transform dither modulation st dm watermarking in the presence of two important classes of non additive attacks such as the gain attack plus noise addition and the quantization attack are evaluated the analysis is developed under the assumption that the host features are independent and identically distributed gaussian random variables and that a minimum distance criterion is used to decode the hidden information the theoretical bit error probabilities are derived in closed form thus permitting to evaluate the impact of the considered attacks on the watermark at a theoretical level the analysis is validated by means of extensive monte carlo simulations in addition to the validation of the theoretical analysis monte carlo simulations permitted to abandon the hypothesis of normally distributed host features in favor of more realistic models adopting a laplacian or a generalized gaussian probability density function the general result of our analysis is that the excellent performance of st dm are confirmed in all cases with the only noticeable exception of the gain attack

a comparison of high order time integrators for thermal convection in rotating spherical shells a numerical study of several time integration methods for solving the three dimensional boussinesq thermal convection equations in rotating spherical shells is presented implicit and semi implicit time integration techniques based on backward differentiation and extrapolation formulae are considered the use of krylov techniques allows the implicit treatment of the coriolis term with low storage requirements the codes are validated with a known benchmark and their efficiency is studied the results show that the use of high order methods especially those with time step and order control increase the efficiency of the time integration and allows to obtain more accurate solutions

explicit form and efficient computation of mls shape functions and their derivatives this work presents a general and efficient way of computing both diffuse and full derivatives of shape functions for meshless methods based on moving least squares approximation mls and interpolation it is an extension of the recently introduced consistency approach based on lagrange multipliers which provides a general framework for constrained mls along with robust algorithms for the computation of shape functions and their diffuse derivatives the particularity of the proposed algorithms is that they do not involve matrix inversion or linear system solving the previous approach is limited to diffuse derivatives of the shape functions and not their full derivatives which are usually much more expensive to obtain in the present paper we propose to efficiently compute the full derivatives by a new algorithm based on the formal differentiation of the previous one in this way we obtain a unified low cost consistent methodology for evaluating the shape functions and both their diffuse and full derivatives in the second part of the paper we introduce explicit forms of mls shape functions in 1d 2d and 3d for an arbitrary number of nodes these forms are especially useful for comparing finite element and mls approximations finally we present a general architecture of an mls program copyright 2000 john wiley sons ltd

modelling three dimensional piece wise homogeneous domains using the α shape based natural element method in this paper the application of the natural element method nem to the numerical analysis of two and three dimensional piece wise homogeneous domains is presented the nem differs from other meshless methods in its capability to accurately reproduce essential boundary conditions along convex boundaries the shape based extension of this method nem generalizes this behaviour to non convex domains enables us to construct models entirely in terms of the initial cloud of points and allows us to simulate material discontinuities in a straightforward manner in the following sections simple and effective algorithms are presented for the construction of shapes in domains composed of various materials examples are presented in two and three dimensional cases in the context of linear elastostatics showing good performance even with the simple numerical quadrature used copyright 2002 john wiley sons ltd

a mlpg lbie approach in combination with bem abstract the local boundary integral equation lbie approach is a promising meshless method recently proposed as an effective alternative to the boundary element method bem for solving non homogeneous anisotropic and non linear problems since the lbie method utilizes in its weak form fundamental solutions as test functions it can be considered as one of the six meshless local petrov galerkin mlpg methods proposed by atluri and coworkers this explains the use of the initials mlpg lbie in the title of the present paper this work addresses a coupling of a new mlpg lbie method recently proposed by the authors for elastodynamic problems and the bem because both methods conclude to a final system of linear equations expressed in terms of nodal displacement and tractions their combination is accomplished directly with no further transformations as it happens in other mlpg bem formulations as well as in typical hybrid finite element method bem schemes the coupling approach is demonstrated for static and frequency domain elastodynamic problems three representative examples are provided in order to illustrate the achieved accuracy of the proposed here mlpg lbie be methodology

a meshfree method for transverse vibrations of anisotropic plates a meshfree approach called displacement boundary method for anisotropic kirchhoff plate dynamic analysis is presented this method is deduced from a variational principle which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables the discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional the stiffness and mass matrices obtained for the dynamic model are frequency independent symmetric and positive definite and their computation involves boundary integrals of regular kernels only due to its features the final resolving system can be solved with the classical approaches by using standard numerical procedures to assess the formulation the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques the present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach

coupling three field formulation and meshless mixed galerkin methods using radial basis functions in this work we solve the elliptic partial differential equation by coupling the meshless mixed galerkin approximation using radial basis function with the three field domain decomposition method the formulation has been adopted to increase the efficiency of the numerical technique by decreasing the error and dealing with the ill conditioning of the linear system caused by the radial basis function convergence analysis of the coupled technique is treated and numerical results of some solved examples are given at the end of this paper

meshless local boundary integral equation method for 2d elastodynamic problems a new meshless method for solving transient elastodynamic boundary value problems based on the local boundary integral equation lbie method and the moving least squares approximation mls is proposed in this paper the lbie with the mls is applied to both transient and steady state laplace transformed elastodynamics applying the mls approximation for spatially dependent terms in the first approach the lbies are transformed into a system of ordinary differential equations for nodal unknowns this system of ordinary differential equations is solved by the houbolt finite difference scheme in the second formulation the time variable is eliminated by using the laplace transformation unknown laplace transforms of displacements and traction vectors are computed from the lbies with the mls approximation the time dependent values are obtained by the durbin inversion technique copyright 2003 john wiley sons ltd

moving particle finite element method with global smoothness we describe a new version of the moving particle finite element method mpfem that provides solutions within a c 0 finite element framework the finite elements determine the weighting for the moving partition of unity a concept of general shape function is proposed which extends regular finite element shape functions to a larger domain these are combined with shepard functions to obtain a smooth approximation the moving particle finite element method combines desirable features of finite element and meshfree methods the proposed approach in fact can be interpreted as a moving partition of unity finite element method or moving kernel finite element method this method possesses the robustness and efficiency of the c 0 finite element method while providing at least c 1 continuity

least squares collocation meshless method a finite point method least squares collocation meshless method is proposed except for the collocation points which are used to construct the trial functions a number of auxiliary points are also adopted unlike the direct collocation method the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least squares sense the moving least squares interpolant is used to construct the trial functions the computational effort required for the present method is in the same order as that required for the direct collocation while the present method improves the accuracy of solution significantly the proposed method does not require any mesh so that it is a truly meshless method three numerical examples are studied in detail which show that the proposed method possesses high accuracy with low computational effort copyright 2001 john wiley sons ltd

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

new concepts in meshless methods meshless methods have been extensively popularized in literature in recent years due to their flexibility in solving boundary value problems two kinds of truly meshless methods the meshless local boundary integral equation mlbie method and the meshless local petrov galerkin mlpg approach are presented and discussed both methods use the moving least squares approximation to interpolate the solution variables while the mlbie method uses a local boundary integral equation formulation and the mlpg employs a local symmetric weak form the two methods are truly meshless ones as both of them do not need a finite element or boundary element mesh either for purposes of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regularly shaped domains in general spheres in three dimensional problems and their boundaries numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable in essence the present meshless method based on the lswf is found to be a simple efficient and attractive method with a great potential in engineering applications copyright 2000 john wiley sons ltd

meshless local petrov galerkin method for two dimensional nonlinear water wave problems in this paper the meshless local petrov galerkin mlpg method is extended to dealing with nonlinear water wave problems the formulation is based on general fluid governing equations and a time marching procedure at each time step the boundary value problem for the pressure is solved using the mlpg method and the velocity and position of nodes are updated by numerical integration the newly extended method is applied to simulating water waves generated by a wave maker and good agreement with analytical solutions and finite element results is presented

implementation of boundary conditions for meshless methods abstract boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite element like kronecker delta condition furthermore it is frequently desirable especially in fluid mechanics to impose general nonlinear boundary and interface constraints this paper describes a computationally efficient algorithm based on d alembert s principle that can be used for general constraints both in meshless methods and finite elements first a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed subsequently an analogous method is developed for nonlinear constraints special attention is given to imposing general boundary and fluid structure interface conditions on the navier stokes equations in terms of conservative variables numerical results using d alembert s principle with the reproducing kernel particle method rkpm including viscous supersonic flow past a naca 7012 airfoil are shown

coupling of the mesh free finite cloud method with the boundary element method a collocation approach abstract meshless and mesh based methods are among the tools frequently applied in the numerical treatment of partial differential equations pdes this paper presents a coupling of the meshless finite cloud method fcm and the standard mesh based boundary element method bem which is motivated by the complementary properties of both methods while the bem is appropriate for solving linear pdes with constant coefficients in bounded or unbounded domains the fcm is appropriate for either homogeneous inhomogeneous or even nonlinear problems in bounded domains both techniques fcm and bem use a collocation procedure in the numerical approximation no mesh is required in the fcm subdomain and its nodal point distribution is completely independent of the bem subdomain the coupling approach is demonstrated for linear elasticity problems because both fcm and bem employ traction displacement relations no transformations between forces and tractions typical of bem and finite element coupling are needed several numerical examples are given to demonstrate the proposed approach

local radial point interpolation mlrpi method for solving time fractional diffusion wave equation with damping the purpose of the current investigation is to determine numerical solution of time fractional diffusion wave equation with damping for caputo s fractional derivative of order 1 2 a meshless local radial point interpolation mlrpi scheme based on galerkin weak form is analyzed the reason of choosing mlrpi approach is that it does not require any background integrations cells instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape the unconditional stability and convergence with order o 6 2 are proved where is time stepping also several numerical experiments are illustrated to verify theoretical analysis

computation of invariant tori by newton krylov methods in large scale dissipative systems abstract a method to compute invariant tori in high dimensional systems obtained as discretizations of pdes by continuation and newton krylov methods is described invariant tori are found as fixed points of a generalized poincare map so that the dimension of the system of equations to be solved is that of the original system due to the dissipative nature of the problems studied the convergence of the linear solvers is extremely fast the computation of periodic orbits inside the arnold s tongues is also considered thermal convection of a binary mixture of fluids in a rectangular cavity has been used to test the method

the quasi periodic doubling cascade in the transition to weak turbulence abstract the quasi periodic doubling cascade is shown to occur in the transition from regular to weakly turbulent behaviour in simulations of incompressible navier stokes flow on a three periodic domain special symmetries are imposed on the flow field in order to reduce the computational effort thus we can apply tools from dynamical systems theory such as continuation of periodic orbits and computation of lyapunov exponents we propose a model ode for the quasi period doubling cascade which in a limit of a perturbation parameter to zero avoids resonance related problems the cascade we observe in the simulations is then compared to the perturbed case in which resonances complicate the bifurcation scenario in particular we compare the frequency spectrum and the lyapunov exponents the perturbed model ode is shown to be in good agreement with the simulations of weak turbulence the scaling of the observed cascade is shown to resemble the unperturbed case which is directly related to the well known doubling cascade of periodic orbits

swinging atwood machine experimental and numerical results and a theoretical study a swinging atwood machine sam is built and some experimental results concerning its dynamic behaviour are presented experiments clearly show that pulleys play a role in the motion of the pendulum since they can rotate and have non negligible radii and masses equations of motion must therefore take into account the moment of inertia of the pulleys as well as the winding of the rope around them their influence is compared to previous studies a preliminary discussion of the role of dissipation is included the theoretical behaviour of the system with pulleys is illustrated numerically and the relevance of different parameters is highlighted finally the integrability of the dynamic system is studied the main result being that the machine with pulleys is non integrable the status of the results on integrability of the pulley less machine is also recalled

machine learning based adaptive watermark decoding in view of anticipated attack we present an innovative scheme of blindly extracting message bits when a watermarked image is distorted in this scheme we have exploited the capabilities of machine learning ml approaches for nonlinearly classifying the embedded bits the proposed technique adaptively modifies the decoding strategy in view of the anticipated attack the extraction of bits is considered as a binary classification problem conventionally a hard decoder is used with the assumption that the underlying distribution of the discrete cosine transform coefficients do not change appreciably however in case of attacks related to real world applications of watermarking such as jpeg compression in case of shared medical image warehouses these coefficients are heavily altered the sufficient statistics corresponding to the maximum likelihood based decoding process which are considered as features in the proposed scheme overlap at the receiving end and a simple hard decoder fails to classify them properly in contrast our proposed ml decoding model has attained highest accuracy on the test data experimental results show that through its training phase our proposed decoding scheme is able to cope with the alterations in features introduced by a new attack consequently it achieves promising improvement in terms of bit correct ratio in comparison to the existing decoding scheme

modeling transient elastodynamic problems using a novel semi analytical method yielding decoupled partial differential equations abstract in this paper a novel semi analytical method is proposed for modeling of two dimensional 2d elastodynamic problems in this regard the domain boundary of the problem is discretized by specific non isoparametric elements that are proposed for the first time in this paper in these elements special shape functions as well as higher order chebyshev mapping functions are implemented for the shape functions kronecker delta property is satisfied for displacement function and its derivatives simultaneously moreover the first derivatives of shape functions are assigned to zero at any given node finally using a weak form of weighted residual method and implementing clenshaw curtis numerical integration coefficient matrices of the system of equations are converted into diagonal ones which leads to a set of decoupled partial differential equations for solving the whole system this means that the governing partial differential equation for each degree of freedom dof becomes independent from other dofs of the domain also to assess the accuracy and efficiency of the proposed method four benchmark problems of 2d elastodynamics are solved using a few numbers of dofs the numerical results present excellent agreement with the analytical solutions and the results from other numerical methods

from steady solutions to chaotic flows in a rayleigh benard problem at moderate rayleigh numbers abstract the dynamics of a rayleigh benard convection problem in a cubical cavity at moderate values of the rayleigh number ra 10 5 and a prandtl number of pr 0 71 with extensions to pr 0 75 and 0 80 was investigated the cubical cavity was heated from below and had perfectly conducting sidewalls and uniform temperature distributions on the two horizontal walls a system of ordinary differential equations with a dimension of typically n 11 000 was obtained when the conservation equations were discretized by means of a galerkin method previous knowledge of the bifurcation diagram of steady solutions reported in the literature was used to identify the origin of several branches of periodic orbits that were continued with ra half a dozen of such periodic orbits were found to be stable within narrow ranges of ra at most some 5000 units wide an attracting two torus restricted to a very narrow region of ra was also identified it was found that the instabilization of periodic orbits quite often resulted into the development of complex dynamics such as the creation of homoclinic and heteroclinic orbits instances of both types of global bifurcations were analyzed in some detail one particular instance of chaotic dynamics a strange attractor was also identified chaotic dynamics has been found at pr 0 71 in a flow invariant subspace which can be interpreted as a fixed point subspace in terms of equivariant theory this subspace is not attracting however some regions of attracting chaotic dynamics for moderate rayleigh numbers 9 10 4 r a 10 5 were found at values of pr slightly above 0 71 the role of a particular homoclinic solution found at pr 0 71 in the generation of these chaotic regions was analyzed