strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

solving time dependent engineering problems with multiquadrics abstract this paper deals with the solution of time dependent problems the multiquadric radial basis function method is formulated with a new approach for transient problems one and two dimensional problems are considered the forward difference and the crank nicolson time marching schemes for parabolic cases are considered the central difference integration method of the newmark family is considered for hyperbolic problems the method proves its accuracy in four numerical examples

energy stable and high order accurate finite difference methods on staggered grids for wave propagation over distances of many wavelengths high order finite difference methods on staggered grids are widely used due to their excellent dispersion properties however the enforceme

survival probability of a doorway state in regular and chaotic environments we calculate the survival probability of a special state which couples randomly to a regular or chaotic environment the environment is modeled by a suitably chosen random matrix ensemble the exact results exhibit non perturbative features as revival of probability and non ergodicity the role of background complexity and coupling complexity is discussed as well

averages of characteristic polynomials in random matrix theory we compute averages of products and ratios of characteristic polynomials associated with orthogonal unitary and symplectic ensembles of random matrix theory the pfaffian determinantal formulae for these averages are obtained and the bulk scaling asymptotic limits are found for ensembles with gaussian weights classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation we employ a discrete approximation method the problem is solved for discrete analogues of random matrix ensembles originating from representation theory and then a limit transition is performed exact pfaffian determinantal formulae for the discrete averages are proven using standard tools of linear algebra no application of orthogonal or skew orthogonal polynomials is needed 2005 wiley periodicals inc

parallel computation of meshless methods for explicit dynamic analysis a parallel computational implementation of modern meshless methods is presented for explicit dynamic analysis the procedures are demonstrated by application of the reproducing kernel particle method rkpm aspects of a coarse grain parallel paradigm are detailed for a lagrangian formulation using model partitioning integration points are uniquely defined on separate processors and particle definitions are duplicated as necessary so that all support particles for each point are defined locally on the corresponding processor several partitioning schemes are considered and a reduced graph based procedure is presented partitioning issues are discussed and procedures to accommodate essential boundary conditions in parallel are presented explicit mpi message passing statements are used for all communications among partitions on different processors the effectiveness of the procedure is demonstrated by highly deformable inelastic example problems

stability and convergence of staggered runge kutta schemes for semilinear wave equations a staggered runge kutta staggered rk scheme is a runge kutta type scheme using a time staggered grid as proposed by ghrist et al in 2000 6 afterwards verwer in two papers investigated the efficiency of a scheme proposed by ghrist et al 6 for linear wave equations we study stability and convergence properties of this scheme for semilinear wave equations in particular we prove convergence of a fully discrete scheme obtained by applying the staggered rk scheme to the mol approximation of the equation

a staggered fourth order accurate explicit finite difference scheme for the time domain maxwell s equations abstract we consider a model explicit fourth order staggered finite difference method for the hyperbolic maxwell s equations appropriate fourth order accurate extrapolation and one sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces an eigenvalue analysis of the overall scheme provides a necessary but not sufficient stability condition and indicates long time stability numerical results verify both the stability analysis and the scheme s fourth order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces for a fixed error level we find the fourth order scheme is computationally cheaper in comparison to the yee scheme by more than an order of magnitude some open problems encountered in the application of such high order schemes are also discussed

superconvergent gradient smoothing meshfree collocation method abstract a superconvergent meshfree collocation method with smoothed nodal gradients is presented in this method the first order smoothed gradients of meshfree shape function are constructed through a meshfree interpolation of the standard derivatives of meshfree shape function while the second order smoothed gradients are computed through directly differentiating the first order smoothed gradients it is noted that the second order smoothed gradients evaluated at meshfree nodes can be conveniently expressed as two successive first order gradient smoothing operations on the meshfree shape function which facilitates a trivial numerical implementation subsequently an employment of the second order smoothed gradients in the strong form of a given problem leads to the gradient smoothing meshfree collocation method purely using nodes as the collocation points based upon a local truncation error analysis it is systematically shown that the proposed meshfree collocation method yields superconvergent solutions for odd degree basis functions a key ingredient attributed to this superconvergence property is that the second order smoothed gradients meet the consistency conditions which go one order beyond the original basis degree of meshfree approximation another interesting fact is that the present formulation enables a convergent collocation scheme when the linear basis function is used in meshfree approximation which is non feasible in the conventional collocation formulation the effectiveness of the proposed methodology is validated by numerical examples for both potential and elasticity problems numerical results well demonstrate the superconvergence and higher efficiency of the present gradient smoothing meshfree collocation method

a general 3d contact smoothing method based on radial point interpolation this paper presents a general 3d contact smoothing method based on the meshfree radial point interpolation method to improve the numerical simulation of contact problems in particular a locally smooth contact surface is constructed from the scattered surface nodes by point interpolation using the combination of polynomial and radial bases with such bases this method reproduces smooth surfaces even for coarse meshes and the constructed surface passes exactly through the surface nodes results for contact problems involving deformable bodies are included to demonstrate its advantages

modeling of piezoelectric transducers with combined pseudospectral and finite difference methods a new hybrid finite difference fd and pseudospectral ps method adapted to the modeling of piezoelectric transducers pzts is presented the time dependent equations of propagation are solved using the ps method while the electric field induced in the piezoelectric material is determined through a fd representation the purpose of this combination is to keep the advantages of both methods in one model the adaptability of fd representation to model piezoelectric elements with various geometries and materials and the low number of nodes per wavelength required by the ps method this approach is implemented to obtain an accurate algorithm to simulate the propagation of acoustic waves over large distances directly coupled to the calculation of the electric field created inside the piezoelectric material which is difficult with classical algorithms these operations are computed using variables located on spatially and temporally staggered grids which attenuate gibbs phenomenon and increase the algorithm s accuracy the two dimensional modeling of a pzt plate excited by a 50 mhz sinusoidal electrical signal is performed the results are successfully compared to those obtained using the finite element fe algorithm of atila software with configurations spatially and temporally adapted to the fe requirements the cost efficiency of the fd ps time domain method is quantified and verified

comparison of taylor finite difference and window finite difference and their application in fdtd the finite difference time domain fdtd method is an important tool in numerical electromagnetic simulation there are many ways to construct a finite difference approximation such as the taylor series expansion theorem the filtering theory etc this paper aims to provide the comparison between the taylor finite difference tfd scheme based on the taylor series expansion theorem and the window finite difference wfd scheme based on the filtering theory their properties have been examined in detail separately in addition the formula of the generalized finite difference gfd scheme is presented which can include both the tfd scheme and the wfd scheme furthermore their application in the numerical solution of maxwell s equations is presented the formulas for the stability criterion and the numerical dispersion relation are derived and analyzed in order to evaluate their performance more accurately a new definition of error is presented upon it the effect of several factors including the grid resolution the courant number and the aspect ratio of the cell on the performance of the numerical dispersion is examined

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

dispersion error reduction for acoustic problems using the edge based smoothed finite element method es fem the paper reports a detailed analysis on the numerical dispersion error in solving 2d acoustic problems governed by the helmholtz equation using the edge based smoothed finite element method es fem in comparison with the standard fem it is found that the dispersion error of the standard fem for solving acoustic problems is essentially caused by the overly stiff feature of the discrete model in such an overly stiff fem model the wave propagates with an artificially higher numerical speed and hence the numerical wave number becomes significantly smaller than the actual exact one owing to the proper softening effects provided naturally by the edge based gradient smoothing operations the es fem model however behaves much softer than the standard fem model leading to the so called very close to exact stiffness therefore the es fem can naturally and effectively reduce the dispersion error in the numerical solution in solving acoustic problems results of both theoretical and numerical studies will support these important findings it is shown clearly that the es fem suits ideally well for solving acoustic problems governed by the helmholtz equations because of the crucial effectiveness in reducing the dispersion error in the discrete numerical model

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

application and optimization of pml abc for the 3 d wave equation in the time domain a three dimensional algorithm with the perfectly matched layer pml absorbing boundary condition abc for the scalar wave equation in the time domain is presented for general inhomogeneous lossy or loss free problems the proposed pml abc is applicable to practical finite difference schemes treating the time domain wave equation such as the time domain wave potential tdwp technique and the time domain scalar wave equation approaches to the analysis of optical structures the time domain wave equation for lossy media is expressed in terms of stretched coordinate variables the algorithm is tested for homogeneous and inhomogeneous media we demonstrate applications to open radiation problems and to port terminations in high frequency circuit problems new pml conductivity profiles are developed for use with the second order wave equation which offer lower reflections in a wider frequency band in comparison with the commonly used in finite difference time domain fdtd algorithms profiles the effect of the termination walls on the overall pml performance is studied and the best choices are singled out

a new support integration scheme for the weakform in mesh free methods a new support integration technique is proposed which is similar to those used in truly mesh free methods the contribution of this paper is to exploit the divergence free condition for the support integrals to construct quadrature formulas that only require three integration points per particle in two dimensions numerical examples show that the proposed integration method can achieve results that agree with manufactured closed form solutions copyright 2009 john wiley sons ltd

a superconvergent point interpolation method sc pim with piecewise linear strain field using triangular mesh a superconvergent point interpolation method sc pim is developed for mechanics problems by combining techniques of finite element method fem and linearly conforming point interpolation method lc pim using triangular mesh in the sc pim point interpolation methods pim are used for shape functions construction and a strain field with a parameter is assumed to be a linear combination of compatible stains and smoothed strains from lc pim we prove theoretically that sc pim has a very nice bound property the strain energy obtained from the sc pim solution lies in between those from the compatible fem solution and the lc pim solution when the same mesh is used we further provide a criterion for sc pim to obtain upper and lower bound solutions intensive numerical studies are conducted to verify these theoretical results and show that 1 the upper and lower bound solutions can always be obtained using the present sc pim 2 there exists an exact 0 1 at which the sc pim can produce the exact solution in the energy norm 3 for any 0 1 the sc pim solution is of superconvergence and 0 is an easy way to obtain a very accurate and superconvergent solution in both energy and displacement norms 4 a procedure is devised to find a prefer 0 1 that produces a solution very close to the exact solution copyright 2008 john wiley sons ltd

a matrix exponential decomposition based time domain method for calculating the defect states of scalar waves in two dimensional periodic structures a time domain method for calculating the defect states of scalar waves in two dimensional 2d periodic structures is proposed in the time stepping process of the proposed method the column vector containing the spatially sampled field values is updated by multiplying it with an iteration matrix which is written in a matrix exponential form the matrix exponential is first computed by using the suzuki s decomposition based technique of the fourth order in which the floquetbloch boundary conditions are incorporated the obtained iteration matrix is then squared to enlarge the time step that can be used in the time stepping process namely the squaring technique and the small nonzero elements in the iteration matrix is finally pruned to improve the sparse structure of the matrix namely the pruning technique the numerical examples of the super cell calculations for 2d defect containing phononic crystal structures show that the fourth order decomposition based technique for the matrix exponential computation is much more efficient than the frequently used precise integration technique pit if the pit is of an order greater than 2 although it is not unconditionally stable the proposed time domain method is particularly efficient for the super cell calculations of the defect states in a 2d periodic structure containing a defect with a wave speed much higher than those of the background materials for this kind of defect containing structures the time stepping process can run stably for a sufficiently large number of the time steps with a time step much larger than the courantfriedrichslewy cfl upper limit and consequently the overall efficiency of the proposed time domain method can be significantly higher than that of the conventional finite difference time domain fdtd method some physical interpretations on the properties of the band structures and the defect states of the calculated periodic structures are also presented

time domain vector potential technique for the meshless radial point interpolation method summary a time domain meshless algorithm based on vector potentials is introduced for the analysis of transient electromagnetic fields the proposed numerical algorithm is a modification of the radial point interpolation method where radial basis functions are used for local interpolation of the vector potentials and their derivatives in the proposed implementation solving the second order vector potential wave equation intrinsically enforces the divergence free property of the electric and magnetic fields furthermore the computational effort associated with the generation of a dual node distribution as required for solving the first order maxwell s equations is avoided the proposed method is validated with several examples of 2d waveguides and filters and the convergence is empirically demonstrated in terms of node density or size of local support domains it is further shown that inhomogeneous node distributions can provide increased convergence rates that is the same accuracy with smaller number of nodes compared with a solution for homogeneous node distribution a comparison of the magnetic vector potential technique with conventional radial point interpolation method is performed highlighting the superiority of the divergence free formulation copyright 2015 john wiley sons ltd

spatial finite difference approximations for wave type equations the simplest finite difference approximations for spatial derivatives are centered explicit and applied to regular equispaced grids well established generalizations include the use of implicit compact approximations and staggered grids we find here that the combination of these two concepts together with high formal order of accuracy is very effective for approximating the first derivatives in space that occur in many wave type pdes

strong convergence of the composite halpern iteration let c be a closed convex subset of a uniformly smooth banach space e and let t c c be a nonexpansive mapping with a nonempty fixed points set given a point u c the initial guess x0 c is chosen arbitrarily and given sequences n n 0 n n 0 and n n 0 in 0 1 the following conditions are satisfied i n 0 n ii n 0 n 0 and 0 a n for some a 0 1 iii n 0 n 1 n n 0 n 1 n and n 0 n 1 n let xn n 1 be a composite iteration process defined by zn nxn 1 n txn yn nxn 1 n tzn xn 1 nu 1 n yn then xn n 1 converges strongly to a fixed point of t

high order finite differences and the pseudospectral method on staggered grids finite difference approximations for the first derivative valid halfway between equidistant gridpoints are in general much more accurate than the corresponding approximations which are valid at gridpoints the pseudospectral fourier method can be viewed as the limit of finite difference approximations when the order of accuracy tends to infinity a fundamentally different and more accurate pseudospectral method is obtained from the halfway approximations this study derives these and related methods and discusses their accuracies

implicit finite difference simulations of seismic wave propagation we propose a new finite difference modeling method implicit both in space and in time for the scalar wave equation we use a three level implicit splitting time integration method for the temporal derivative and implicit finite difference operators of arbitrary order for the spatial derivatives both the implicit splitting time integration method and the implicit spatial finite difference operators require solving systems of linear equations we show that it is possible to merge these two sets of linear systems one from implicit temporal discretizations and the other from implicit spatial discretizations to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm we give the complete derivations of the implicit splitting time integration method and the implicit spatial finite difference operators and present the resulting discretized formulas for the scalar wave equation we conduct a thorough numerical analysis on grid dispersions of this new implicit

time step n tupling for wave equations abstractwe have constructed novel temporal discretizations for wave equations we first select an explicit time integrator that is of second order leading to classic time marching schemes in which the next value of the wavefield at the discrete time t t is computed from current values known at time t and the previous time t t then we determine how the time step can be doubled tripled or generally n tupled producing a new time stepping method in which the next value of the wavefield at the discrete time t n t is computed from current values known at time t and the previous time t n t in between time values of the wavefield are eliminated using the fourier method to calculate space derivatives the new time integrators allow larger stable time steps than traditional time integrators however like the lax wendroff procedure they require more computational effort per time step because the new schemes are developed from the classic second order time stepping scheme they will have the same proper

classroom note calculation of weights in finite difference formulas the classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope e g specialized recursions for centered and staggered approximations for adams bashforth adams moulton and bdf formulas for odes etc two recent algorithms overcome these problems for equispaced grids such weights can be found very conveniently with a two line algorithm when using a symbolic language such as mathematica reducing to one line in the case of explicit approximations for arbitrarily spaced grids we describe a computationally very inexpensive numerical algorithm

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

universal results for correlations of characteristic polynomials riemann hilbert approach we prove that general correlation functions of both ratios and products of characteristic polynomials of hermitian random matrices are governed by integrable kernels of three different types a those constructed from orthogonal polynomials b those constructed from cauchy transforms of the same orthogonal polynomials and finally c those constructed from both orthogonal polynomials and their cauchy transforms these kernels are related with the riemann hilbert problem for orthogonal polynomials for the correlation functions we obtain exact expressions in the form of determinants of these kernels derived representations enable us to study asymptotics of correlation functions of characteristic polynomials via the deift zhou steepest descent stationary phase method for riemann hilbert problems and in particular to find negative moments of characteristic polynomials this reveals the universal parts of the correlation functions and moments of characteristic polynomials for an arbitrary invariant ensemble of 2 symmetry class

a vector meshless parabolic equation method for three dimensional electromagnetic scatterings the three dimensional 3 d vector parabolic equation pe method was used for electromagnetic scattering with reasonable accuracy the algorithm was marched from plane to plane along some preferred directions so that the computational load could be reduced significantly however the traditional 3 d pe method was discretized with the finite difference fd scheme and was not flexible for complex geometries in this paper the radial point interpolation meshless rpim method is used for its flexibility to model complex geometries in each transverse plane when the pe method is applied to analyze the electromagnetic scattering from electrically large objects numerical results demonstrate that the proposed technique can efficiently give reasonably accurate results for the complex objects when compared with both the multilevel fast multipole method mlfmm and the traditional pe method

a point interpolation meshless method based on radial basis functions a point interpolation meshless method is proposed based on combining radial and polynomial basis functions involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis this non singularity is useful in constructing well performed shape functions furthermore the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property this makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least squares approximation in addition the partial derivatives of shape functions are easily obtained thus improving computational efficiency examples on curve surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high copyright 2002 john wiley sons ltd

radial point interpolation based finite difference method for mechanics problems a radial point interpolation based finite difference method rfdm is proposed in this paper in this novel method radial point interpolation using local irregular nodes is used together with the conventional finite difference procedure to achieve both the adaptivity to irregular domain and the stability in the solution that is often encountered in the collocation methods a least square technique is adopted which leads to a system matrix with good properties such as symmetry and positive definiteness several numerical examples are presented to demonstrate the accuracy and stability of the rfdm for problems with complex shapes and regular and extremely irregular nodes the results are examined in detail in comparison with other numerical approaches such as the radial point collocation method that uses local nodes conventional finite difference and finite element methods copyright 2006 john wiley sons ltd

a linearly conforming point interpolation method lc pim for three dimensional elasticity problems linearly conforming point interpolation method lc pim is formulated for three dimensional elasticity problems in this method shape functions are generated using point interpolation method by adopting polynomial basis functions and local supporting nodes are selected based on the background cells the shape functions so constructed have the kronecker delta functions property and it allows straightforward imposition of point essential boundary conditions galerkin weak form is used for creating discretized system equations and a nodal integration scheme with strain smoothing operation is used to perform the numerical integration the present lc pim can guarantee linear exactness and monotonic convergence for the numerical results numerical examples are used to examine the present method in terms of accuracy convergence and efficiency compared with the finite element method using linear elements the lc pim can achieve better efficiency and higher accuracy especially for stresses copyright 2007 john wiley sons ltd

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

pricing european and american options by radial basis point interpolation a rbpi method for pricing european and american options is proposed rbpi has not yet been used for option pricing the overall efficiency is improved by coupling rbpi with other approaches three different algorithms for american options are tested and compared numerical results demonstrate the effectiveness of the techniques employed we propose the use of the meshfree radial basis point interpolation rbpi to solve the black scholes model for european and american options the rbpi meshfree method offers several advantages over the more conventional radial basis function approximation nevertheless it has never been applied to option pricing at least to the very best of our knowledge in this paper the rbpi is combined with several numerical techniques namely an exponential change of variables which allows us to approximate the option prices on their whole spatial domain a mesh refinement algorithm which turns out to be very suitable for dealing with the non smooth options payoff and an implicit euler richardson extrapolated scheme which provides a satisfactory level of time accuracy finally in order to solve the free boundary problem that arises in the case of american options three different approaches are used and compared the projected successive overrelaxation method psor the bermudan approximation and the penalty approach numerical experiments are presented which demonstrate the computational efficiency of the rbpi and the effectiveness of the various techniques employed

stability of explicit time discretizations for solving initial value problems stability regions of explicit linear time discretization methods for solving initial value problems are treated if an integration method needsm function evaluations per time step then we scale the stability region by dividing bym we show that the scaled stability region of a method satisfying some reasonable conditions cannot be properly contained in the scaled stability region of another method bounds for the size of the stability regions for three different purposes are then given for general nonlinear ordinary differential systems for systems obtained from parabolic problems and for systems obtained from hyperbolic problems we also show how these bounds can be approached by high order methods

a new hybrid boundary node method based on taylor expansion and the shepard interpolation method summary a novel meshless method based on the shepard and taylor interpolation method stim and the hybrid boundary node method hbnm is proposed based on the shepard interpolation method and taylor expansion the stim is developed to construct the shape function of the hbnm in the stim the shepard shape function is used as the basic function which is the zero level shape function and the high power basic functions are constructed through taylor expansion four advantages of the stim are the interpolation property the arbitrarily high order consistency the absence of inversion for the whole process of shape function construction and the low computational expense these properties are desirable in the implementation of meshless methods by combining the stim and the hbnm a much more effective meshless method is proposed to solve the elasticity problems compared with the traditional hbnm the stim can improve accuracy because of the use of high power basic functions and can also improve the computational efficiency because there is no inversion for the shape function construction process numerical examples are given to demonstrate the accuracy and efficiency of the proposed method copyright 2015 john wiley sons ltd

free vibration analysis of fg cntrc shell structures using the meshfree radial point interpolation method abstract this study conducts the first known free vibration analysis of functionally graded carbon nanotubes reinforced fg cntrc shell structures using the meshfree radial point interpolation method rpim the modified first order shear deformation theory modified fsdt is implemented to get the realistic effect of the transverse shear deformation with its parabolic distribution numerical examples are carried out to examine the convergence and accuracy of the element free rpim method in its application to the free vibration fg cntrc analysis of shell structures results obtained using the proposed meshfree method demonstrate that the improved fsdt is very successful compared to closed form solutions and finite element results using different shell theories

convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings in this paper we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of banach spaces our results presented in this paper improve and extend the recent ones announced by many others

a point interpolation method for simulating dissipation process of consolidation abstract a biot s consolidation problem in foundation engineering is numerically investigated using improved point interpolation method pim a weak form of biot s theory is first developed to consider the unbalanced forces at previous time step and thus guarantees the global equilibrium at current step two independent variables in the weak form displacement and excess pore water pressure are approximated using the same shape functions through pim technique the pim technique constructs its interpolation functions through a cluster of scattered points in problem domain and its shape function is of delta properties thus implementation of essential boundary conditions is as easy as in conventional finite element method crank nicholson s integration scheme is used to discretize time domain finally examples are studied and compared with finite element methods to demonstrate its capability

a locking free meshfree method for the simulation of shear deformable plates based on a mixed variational formulation abstract the problem of shear locking in the thin plate limit is a well known issue that must be overcome when discretising the reissner mindlin plate equations in this paper we present a shear locking free method utilising meshfree maximum entropy basis functions and rotated raviart thomas nedelec elements within a mixed variational formulation the formulation draws upon well known techniques in the finite element literature due to the inherent properties of the maximum entropy basis functions our method allows for the direct imposition of dirichlet essential boundary conditions in contrast to methods based on moving least squares basis functions we present benchmark problems that demonstrate the accuracy and performance of the proposed method

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

staggered time integrators for wave equations we consider variations of the adams bashforth backward differentiation and runge kutta families of time integrators to solve systems of linear wave equations on uniform time staggered grids these methods are found to have smaller local truncation errors and to allow larger stable time steps than traditional nonstaggered versions of equivalent orders we investigate the accuracy and stability of these methods analytically experimentally and through the use of a novel root portrait technique

regular article a fast spectral algorithm for nonlinear wave equations with linear dispersion spectral algorithms offer very high spatial resolution for a wide range of nonlinear wave equations on periodic domains including well known cases such as the korteweg de vries and nonlinear schrodinger equations for the best computational efficiency one needs also to use high order methods in time while somehow bypassing the usual severe stability restrictions we use linearly implicit multistep methods with the innovation of choosing different methods for different ranges in fourier space high accuracy at low wavenumbers and a stability at high wavenumbers this new approach compares favorably to alternatives such as split step and integrating factor or linearly exact methods

overlapping and non overlapping domain decomposition methods for large scale meshless efg simulations abstract meshless methods have a number of virtues in problems concerning crack growth and propagation strain localization dynamic shear band propagation projectile penetration among others the main drawback of such methods is that the resulting matrices are more densely populated and the computational cost for the formulation and solution of the problem is much higher than the conventional fem this is the reason for their limited application to academic and small scale problems until now in this paper we introduce a novel approach for reducing the computational cost of meshless element free galerkin efg methods by employing domain decomposition techniques on the physical as well as on the algebraic domains specifically we propose the implementation of the dual domain decomposition feti family of methods that have been successfully used with fem in many problems in computational mechanics we address the issues of dividing an overlapping meshfree efg domain to several overlapping subdomains following the algebraic decomposition of the feti method and alternatively on non overlapping subdomains by modifying the required displacement compatibility conditions and by improving the accuracy of the solution through a stress update procedure

a g space theory and a weakened weak w2 form for a unified formulation of compatible and incompatible methods part i theory this paper introduces a g space theory and a weakened weak form w2 using the generalized gradient smoothing technique for a unified formulation of a wide class of compatible and incompatible methods the w2 formulation works for both finite element method settings and mesh free settings and w2 models can have special properties including softened behavior upper bounds and ultra accuracy part i of this paper focuses on the theory and fundamentals for w2 formulations a normed g space is first defined to include both continuous and discontinuous functions allowing the use of much more types of methods techniques to create shape functions for numerical models important properties and a set of useful inequalities for g spaces are then proven in the theory and analyzed in detail these properties ensure that a numerical method developed based on the w2 formulation will be spatially stable and convergent to the exact solutions as long as the physical problem is well posed the theory is applicable to any problems to which the standard weak formulation is applicable and can offer numerical solutions with special properties including close to exact stiffness upper bounds and ultra accuracy copyright 2009 john wiley sons ltd

characteristic polynomials of random matrices at edge singularities we have discussed earlier the correlation functions of the random variables mathrm det ensuremath lambda ensuremath x in which x is a random matrix in particular the moments of the distribution of these random variables are universal functions when measured in the appropriate units of the level spacing when the ensuremath lambda mathrm s instead of belonging to the bulk of the spectrum approach the edge a crossover takes place to an airy or to a bessel problem and we consider here these modified classes of universality furthermore when an external matrix source is added to the probability distribution of x various different phenomenona may occur and one can tune the spectrum of this source matrix to other critical points again there are remarkably simple formulas for arbitrary source matrices which allow us to compute the moments of the characteristic polynomials in these cases as well

a rescaled localized radial basis function interpolation on non cartesian and nonconforming grids in this paper we propose a rescaled localized radial basis function rl rbf interpolation method based on the use of compactly supported radial basis functions starting from the classical rbf interpolation technique we introduce a rescaling that allows for exact interpolation of constant fields between nonconforming meshes without the use of an extra polynomial term we also present two dimensional and three dimensional numerical examples on arbitrary finite element meshes to show that the rl rbf interpolation leads to accurate results fast evaluation and easy parallelization of the algorithm all the computations are carried out using the open source finite element library lifev

derivation of determinantal structures for random matrix ensembles in a new way there are several methods to treat ensembles of random matrices in symmetric spaces circular matrices chiral matrices and others orthogonal polynomials and the supersymmetry method are particular powerful techniques here we present a new approach to calculate averages over ratios of characteristic polynomials at first sight paradoxically one can call our approach supersymmetry without supersymmetry because we use structures from supersymmetry without actually mapping onto superspaces we address two kinds of integrals which cover a wide range of applications for random matrix ensembles for probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way as a new application we derive an expression for the k point correlation function of an arbitrary rotation invariant probability density over the hermitian matrices in the presence of an external field

hybrid time domain solvers for the maxwell equations in 2d numerical simulation is an important tool in understanding the electromagnetic field and how it interacts with the environment different topics for time domain finite difference fdtd and finite element fetd methods for maxwell s equations are treated in this thesis subcell models are of vital importance for the efficient modeling of small objects that are not resolved by the grid a novel model for thin sheets using shell elements is proposed this approach has the advantage of taking into account discontinuities in the normal component of the electric field unlike previous models based on impedance boundary conditions ibcs several results are presented to illustrate the capabilities of the shell element approach waveguides are of fundamental importance in many microwave applications for example in antenna feeds the key issues of excitation and truncation of waveguides are addressed a complex frequency shifted form of the uniaxial perfectly matched layer upml absorbing boundary condition abc in fetd is developed prism elements are used to promote automatic grid generation and enhance the performance results are presented where reflection errors below 70db are obtained for different types of waveguides including inhomogeneous cases excitation and analysis via the scattering parameters are achieved using waveguide modes computed by a general frequency domain mode solver for the vector helmholtz equation huygens surfaces are used in both fdtd and fetd for excitation in waveguide ports inverse problems have received an increased interest due to the availability of powerful computers an important application is non destructive evaluation of material a time domain minimization approach is presented where exact gradients are computed using the adjoint problem the approach is applied to a general form of maxwell s equations including dispersive media and upml successful reconstruction examples are presented both using synthetic and experimental measurement data parameter reduction of complex geometries using simplified models is an interesting topic that leads to an inverse problem gradients for subcell parameters are derived and a successful reconstruction example is presented for a combined dielectric sheet and slot geometry

a new method for evaluating options based on multiquadric rbf fd method abstract in this paper a new local meshless approach based on radial basis functions rbfs is presented to price the options under the black scholes model the global rbf approximations derived from the conventional global collocation method usually lead to ill conditioned matrices employing the idea of local approximants of the finite difference fd method and combining it with the radial basis function rbf method can result in a local meshless approach such as rbf fd it removes the difficulty of ill conditionness of the original method the new proposed approach is unconditionally stable as it is shown by von neumann stability analysis it is fast and produces high accurate results as shown in numerical experiments moreover we took into account the variation of shape parameter and analyzed numerically the behavior of the rbf fd method

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

meshless implementation of arbitrary 3d shell structures based on a modified first order shear deformation theory abstract a meshless implementation of arbitrary 3d shell structures based on a modified first order shear deformation theory fsdt is investigated in this paper the fsdt is improved in this manuscript in order to assume a parabolic distribution of the shear strain to correct the constant shear stress in the mindlin reissner theory and to get closer to a realistic distribution of the shear strain through the thickness the radial point interpolation method is used in the construction of shape functions based on arbitrarily distributed nodes of general spatial shell geometry the convergence of the proposed model is compared to other well known formulations found in the literature considering isotropic and functionally graded spatial shell structures the results obtained using the proposed meshless method demonstrate that the improved fsdt is very successful compared to closed form solutions and finite element results using different shell theories the effect of the material distribution on the deflections and stresses is also analyzed

convergence theorems of common fixed points for a family of lipschitz quasi pseudocontractions abstract in an infinite dimensional hilbert space the normal mann s iteration has only weak convergence in general even for nonexpansive mappings the purpose of this paper is to modify the normal mann s iteration to have strong convergence for a family of lipschitz quasi pseudocontractions in the framework of hilbert spaces our results improve and extend the corresponding ones announced by many others

meshless galerkin methods using radial basis functions we combine the theory of radial basis functions with the field of galerkin methods to solve partial differential equations after a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions

analysis of transient response of saturated porous elastic soil under cyclic loading using element free galerkin method a two dimensional numerical procedure is presented to analyse the transient response of saturated porous elastic soil layer under cyclic loading the procedure is based on the element free galerkin method and incorporated into the periodic conditions temporal and spatial periodicity its shape function is constructed by moving least square approximants essential boundary conditions are implemented through lagrange multipliers and the periodic conditions are implemented through a revised variational formulation time domain is discretized through the crank nicolson scheme analytical solutions are developed to assess the effectiveness and accuracy of the current procedure in one and two dimensions for only temporal periodic problems a one dimensional transient problem of finite thickness soil layer is analysed for sinusoidal surface loading for both temporal and spatial periodic problems a typical two dimensional wave induced transient problem with the seabed of finite thickness is analysed finally a moving boundary problem is analysed it is found that the current procedure is simple efficient and accurate in predicting the response of soil layer under cyclic loading 2002 elsevier science ltd all rights reserved

numerical integration of damped maxwell equations we study the numerical time integration of maxwell s equations from electromagnetism following the method of lines approach we start from a general semidiscrete maxwell system for which a number of time integration methods are considered these methods have in common an explicit treatment of the curl terms central in our investigation is the question how to efficiently raise the temporal convergence order beyond the standard order of two in particular in the presence of an explicitly or implicitly treated damping term which models conduction

a point interpolation method with least square strain field pim lss for solution bounds and ultra accurate solutions using triangular mesh abstract a point interpolation method with least square strain field pim lss is developed for solid mechanics problems using triangular background mesh in the pim lss pim shape functions are used for displacement field construction that may or may not be compatible and a least square fitting technique is adopted to construct the strain field a strain constructed galerkin sc galerkin weak formulation is then proposed for establishing discretized pim lss models that have a number of special properties we proved theoretically 1 the pim lss provides a softening effect to the fem model and a stiffing effect to the node based smoothed point interpolation method ns pim model 2 the exact solution is bounded from both by pim lss solutions with strain field of zero order fitting and that with higher order fitting 3 there exists a preferred order of fitting for the strain field such that ultra accurate one order higher accuracy solution can be obtained using the pim lss these theorems and properties have been confirmed in numerical examples

on the optimal shape parameters of radial basis functions used for 2 d meshless methods abstract a radial point interpolation meshless or radial pim method was proposed by authors to overcome the possible singularity associated with only polynomial basis the radial pim used multiquadric mq or gaussian as basis functions these two radial basis functions all included shape parameters although choice of shape parameters has been a hot topic in approximation theory and some empirical formulae were proposed how these shape parameters affect the accuracy of the radial pim has not been studied yet this paper studied the effect of shape parameters on the numerical accuracy of radial pim a range of suitable shape parameters is obtained from the analysis of the condition number of the system matrix error of energy and irregularity of node distribution it is observed that the widely used shape parameters for mq and reciprocal mq basis are not even close to their optimums the optimal shape parameters are found in this paper to be simply q 1 03 and r 1 42 for mq basis and c 0 003 0 03 for gaussian basis

a first order k space model for elastic wave propagation in heterogeneous media a pseudospectral model of linear elastic wave propagation is described based on the first order stress velocity equations of elastodynamics k space adjustments to the spectral gradient calculations are derived from the dyadic green s function solution to the second order elastic wave equation and used to a ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size and b also allows larger time steps without loss of accuracy in heterogeneous media the formulation in k space allows the wavefield to be split easily into compressional and shear parts a perfectly matched layer pml absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield the staggered grid which is essential for accurate simulations is described along with other practical details of the implementation the model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems the efficiency of the model is by virtue of the reduced point per wavelength requirement the use of the fast fourier transform fft to calculate the gradients in k space and larger time steps made possible by the k space adjustments

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

two dimensional axisymmetric numerical simulation of supercritical phase conjugation of ultrasound in active solid media in the present study a two dimensional axisymmetric numerical model is developed for supercritical parametric phase conjugation of ultrasound in a solid active element of cylindrical shape and finite length the pseudospectral time domain algorithm pstd is used owing to its efficiency to model large scale problems pstd solves elastic wave equation in time dependent heterogeneous isotropic and axisymmetric anisotropic solids using ffts for high order approximation of the spatial differential operator on staggered grid and a fourth order adams bashforth time integrator in order to truncate the computational domain absorbing boundary conditions are introduced with complex frequency shifted perfectly matched layers this procedure is highly effective at absorbing signals of long time signature the free surface of the active ceramic rod is introduced through the method of images a systematic study of the influence of lateral limitations of the active medium on parametric wave phase conjugation of sound

moments of the derivative of characteristic polynomials with an application to the riemann zeta function we investigate the moments of the derivative on the unit circle of characteristic polynomials of random unitary matrices and use this to formulate a conjecture for the moments of the derivative of the riemann function on the critical line we do the same for the analogue of hardy s z function the characteristic polynomial multiplied by a suitable factor to make it real on the unit circle our formulae are expressed in terms of a determinant of a matrix whose entries involve the i bessel function and alternately by a combinatorial sum

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

generalized finite element method for vector electromagnetic problems the generalized finite element method gfem as introduced by babuska is a partition of unity framework for solving scalar partial differential equations pdes to date they have been applied extensively to the solution of elliptic and parabolic pdes this technique can be interpreted as a unified prescription of a host of well known techniques such as classical finite element methods that are based on tessellation point cloud techniques and element free galerkin methods the focus of this paper is to extend this technique to solve vector electromagnetic problems however modification of gfem to address this problem poses a novel set of challenges i the vector nature of the problem and the different continuity requirements on each component imply that basis functions developed should share similar characteristics ii the basis functions have to be able to represent divergence free electromagnetic fields in a source free region when they themselves are not divergence free these have been the primary impediments to extension of this technique in this paper we propose a method that may be used to overcome these obstacles and will demonstrate h and p convergence characteristics of the proposed method for a range of problems finally we will demonstrate convergence characteristics of this technique for analyzing scattering from a sharp wedge when the basis functions include analytical local field representation

new correlation functions for random matrices and integrals over supergroups the averages of ratios of characteristic polynomials det x of n n random matrices x are investigated in the large n limit for the gue goe and gse ensembles the density of states and the two point correlation function are derived from these ratios the method relies on an extension of the harish chandra itzykson zuber integrals to the goe ensemble and to supergroups which are explicitly computed through heat kernel differential equations an external matrix source linearly coupled to the random matrices may also be added to the gaussian distribution and allows for a discussion of the universality of the goe results in the large n limit

on the averages of characteristic polynomials from classical groups we provide an elementary and self contained derivation of formulae for averages of products and ratios of characteristic polynomials of random matrices from classical groups using classical results due to weyl and littlewood

integration free coons macroelements for the solution of 2d poisson problems large isoparametric macroelements with closed form cardinal global shape functions under the label coons patch macroelements cpm have been previously proposed and used in conjunction with the finite element method and the boundary element method this paper continues the research on the performance of cpm in conjunction with the collocation method in contrast to the previous cpm that was based on a galerkin ritz formulation no domain integration is now required a fact that justifies the name integration free coons macroelements therefore in addition to avoiding mesh generation and saving human effort the proposed technique has the additional advantage of further reducing the computer effort the theory is supported by five test cases concerning poisson and laplace problems within 2d smooth quadrilateral domains copyright 2008 john wiley sons ltd

a point interpolation method for two dimensional solids a point interpolation method pim is presented for stress analysis for two dimensional solids in the pim the problem domain is represented by properly scattered points a technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points the pim equations are then derived using variational principles in the pim the essential boundary conditions can be implemented with ease as in the conventional finite element methods the present pim has been coded in fortran the validity and efficiency of the present pim formulation are demonstrated through example problems it is found that the present pim is very easy to implement and very flexible for obtained displacements and stresses of desired accuracy in solids as the elements are not used for meshing the problem domain the present pim opens new avenues to develop adaptive analysis codes for stress analysis in solids and structures copyright 2001 john wiley sons ltd

frequency dispersive materials for 3 d hybrid solvers in time domain the recursive convolution method to treat linear dispersive materials in the finite difference time domain fdtd is here generalized to an explicit finite volume solver and an implicit finite element solver both solvers are interfaced to fdtd resulting in two hybrid solvers the stability of the solvers is analyzed and the accuracy is demonstrated in several scattering cases where a plane wave illuminates a sphere with complex permittivity excellent agreement with the analytical mie series solution is obtained for materials of debye and lorentz type as well as for a material consisting of two lorentz poles

stability and numerical dispersion analysis of a fourth order accurate fdtd method in order to obtain high order accuracy a fourth order accurate finite difference time domain fdtd method is presented by kyu pyung hwang unlike conventional fdtd methods a staggered backward differentiation scheme instead of the leapfrog scheme is used to approximate the temporal partial differential operator however the high order of its characteristic equation derived by the von neumann method makes the analysis of its numerical dispersion and stability very difficult in automatic control theory there are two effective methods for the stability analysis i e the routh hurwitz test and the jury test the combination of the von neumann method with each of the two can strictly derive the stability condition which only makes use of the coefficients of its characteristic equation without numerically solving it the method of analysis in this paper is also applicable in the stability and numerical analysis of other high order accurate fdtd methods

convergence of a general iterative method for nonexpansive mappings in hilbert spaces in this paper we introduce a modified ishikawa iterative process for approximating a fixed point of nonexpansive mappings in hilbert spaces we establish some strong convergence theorems of the general iteration scheme under some mild conditions the results improve and extend the corresponding results of many others

a modified finite particle method multi dimensional elasto statics and dynamics summary particle methods are a class of numerical methods that belong to the family of meshless methods and are not based on an underlying mesh or grid but rather on any general distribution of particles they are nowadays widely applied in many fields including for example solid mechanics fluid dynamics and thermodynamics in this paper we start from the original formulation of the so called modified finite particle method mfpm and develop a novel formulation in particular after discussing the position of the mfpm in the context of the existing literature on meshless methods and recalling and discussing the 1d formulation and its properties we introduce the novel formulation along with its extension to the approximation of 2d and 3d differential operators we then propose applications of the discussed methods to some elastostatic and elastodynamic problems the obtained results confirm the potential and the flexibility of the considered methods as well as their second order accuracy proposing mfpm as a viable alternative for the simulation of solids and structures copyright 2014 john wiley sons ltd

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

the meshless local petrov galerkin method in two dimensional electromagnetic wave analysis this paper deals with one member of the class of meshless methods namely the meshless local petrov galerkin mlpg method and explores its application to boundary value problems arising in the analysis of two dimensional electromagnetic wave propagation and scattering this method shows some similitude with the widespread finite element method fem like the discretization of weak forms and sparse global matrices mlpg and fem differ in what regards the construction of an unstructured mesh in mlpg there is no mesh just a cloud of nodes without connection to each other spread throughout the domain the suppression of the mesh is counterbalanced by the use of special shape functions constructed numerically this paper illustrates how to apply mlpg to wave scattering problems through a number of cases in which the results are compared either to analytical solutions or to those provided by other numerical methods

application of normalized pseudo laplacian to elastic wave modeling on staggered grids we extended the pseudo laplacian to staggered grids based on the concept of normalized pseudo laplacian and applied it to constructing the pseudoanalytical formulations for the variable density acoustic wave equation and the elastic wave equation acoustic wavefields only contain p waves and therefore only p wave pseudo laplacians are required for acoustic wave propagation in comparison two sets of staggered grid pseudo laplacians are needed in the elastic case in order to properly compensate for time stepping errors for both p waves and s waves we gave a thorough derivation of the pseudoanalytical method for the elastic wave equation based on normalized pseudo laplacians implemented on staggered grids and presented the resulting complete discretized formulas we proved that the staggered grid pseudo laplacian reduces to the pseudo laplacian for the scalar wave equation on standard grids when using zero compensation velocities for normalized pseudo laplacians the pseudoanalytical formulas simply re

two results concerning the stability of staggered multistep methods staggered spatial node layouts are widely used in the context of solving wave equations when this idea of staggering is extended to time integrators for wave equations one finds methods that offer both better accuracy and less restrictive stability conditions for an equivalent computational cost here we prove two results concerning staggered multistep methods we first prove that staggered backwards differentiation methods are unstable for all orders p ge 5 we then extend dahlquist s first stability barrier to explicit staggered multistep methods

replica symmetric approach to the typical eigenvalue fluctuations of gaussian random matrices we discuss an approach to compute the first and second moments of the number of eigenvalues i n that lie in an arbitrary interval of the real line for gaussian random matrices the method combines the standard replica symmetric theory with a perturbative expansion of the saddle point action up to leading to the correct logarithmic scaling of the variance as well as to an analytical expression for the correction to the average standard results for the number variance at the local scaling regime are recovered in the limit of a vanishing interval the limitations of the replica symmetric method are unveiled by comparing our results with those derived through exact methods the present work represents an important step to study the fluctuations of i n in non invariant random matrix ensembles where the joint distribution of eigenvalues is not known