spectral element methods on triangles and quadrilaterals comparisons and applications in this paper we compare a triangle based spectral element method sem with the classical quadrangle based sem and with a standard spectral method for the sake of completeness the triangle sem making use of the fekete points of the triangle is first revisited the requirement of a highly accurate quadrature rule is particularly emphasized then it is shown that the convergence properties of the triangle sem compare well with those of the classical sem by solving an elliptic equation with smooth but steep analytical solution it is also proved numerically that the condition number grows significantly faster for triangles than for quadrilaterals finally the attention is focused on a diffraction problem to show the high flexibility of the triangle sem

use of higher order shape functions in the scaled boundary finite element method the scaled boundary finite element method is a novel semi analytical technique whose versatility accuracy and efficiency are not only equal to but potentially better than the finite element method and the boundary element method for certain problems this paper investigates the possibility of using higher order polynomial functions for the shape functions two techniques for generating the higher order shape functions are investigated in the first the spectral element approach is used with lagrange interpolation functions in the second hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones as in the p version of the finite element method to check the accuracy of the proposed procedures a plane strain problem for which an exact solution is available is employed a more complex example involving three scaled boundary subdomains is also addressed the rates of convergence of these examples under p refinement are compared with the corresponding rates of convergence achieved when uniform h refinement is used allowing direct comparison of the computational cost of the two approaches the results show that it is advantageous to use higher order elements and that higher rates of convergence can be obtained using p refinement instead of h refinement copyright 2005 john wiley sons ltd

on the use of nurbs based discretizations in the scaled boundary finite element method for wave propagation problems abstract we discuss the application of non uniform rational b splines nurbs in the scaled boundary finite element method sbfem for the solution of wave propagation problems at rather high frequencies we focus on the propagation of guided waves along prismatic structures of constant cross section comparisons are made between nurbs based discretizations and high order spectral elements in terms of the achievable convergence rates we find that for the same order of shape functions nurbs can lead to significantly smaller errors compared with lagrange polynomials the difference becomes particularly important at very high frequencies where spectral elements are prone to instabilities furthermore we analyze the behavior of nurbs for the discretization of curved boundaries where the benefit of exact geometry representation becomes crucial even in the low frequency range

unit impulse response matrix of unbounded medium by infinitesimal finite element cell method abstract to calculate the unit impulse response matrix of the unbounded medium the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed a formulation can be derived for acceleration velocity and displacement unit impulse response matrices starting from the acceleration unit impulse impulse response matrix those of the velocity and displacement are constructed the algorithm to determine the acceleration unit impulse response matrix and its application are simpler than the other two alternatives as in the cloning algorithm the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell the derivation is performed exclusively in the time domain at each time station a linear system of equations is solved the consistent boundary method to analyse a layered medium in the frequency domain and the viscous dashpot boundary method are special cases of the infinitesimal finite element cell method the error is governed by the finite element discretization in the circumferential direction as the width of the finite element cell in the radial direction is infinitesimal the infinitesimal finite element cell method is thus exact in the finite element sense the method leads to highly accurate results for a vast class of problems ranging from a one dimensional spherical cavity to a rectangular foundation embedded in a half plane

consistent infinitesimal finite element cell method for diffusion equation in unbounded medium abstract to calculate the unit step response matrix of an unbounded medium for use in a time domain analysis of unbounded medium structure interaction for the diffusion equation the consistent infinitesimal finite element cell method is developed for the three dimensional case its derivation is based on the finite element formulation and on similarity the discretization is only performed on the structure medium interface yielding a reduction of the spatial dimension by 1 the procedure is rigorous in the radial direction and exact in the finite element sense in the circumferential directions in contrast to the boundary element procedure the consistent infinitesimal finite element cell method does not require a fundamental solution and incorporates interfaces extending from the structure medium interface to infinity compatible with similarity without any additional computational effort a general anisotropic material can be processed

logically rectangular grids and finite volume methods for pdes in circular and spherical domains we describe a class of logically rectangular quadrilateral and hexahedral grids for solving pdes in circular and spherical domains including grid mappings for the circle the surface of the sphere and the three dimensional ball the grids are logically rectangular and the computational domain is a single cartesian grid compared to alternative approaches based on a multiblock data structure or unstructured triangulations this approach simplifies the implementation of numerical methods and the use of adaptive refinement a more general domain with a smooth boundary can be gridded by composing one of the mappings from this paper with another smooth mapping from the circle or sphere to the desired domain although these grids are highly nonorthogonal we show that the high resolution wave propagation algorithm implemented in clawpack can be used effectively to approximate hyperbolic problems on these grids since the ratio between the largest and smallest grids is below 2 for most of our grid mappings explicit finite volume methods such as the wave propagation algorithm do not suffer from the center or pole singularities that arise with polar or latitude longitude grids numerical test calculations illustrate the potential use of these grids for a variety of applications including euler equations shallow water equations and acoustics in a heterogeneous medium pattern formation from a reaction diffusion equation on the sphere is also considered all examples are implemented in the clawpack software package and full source code is available on the web along with matlab routines for the various mappings

from electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex the electrostatic interpretation of the jacobi gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex moreover several new estimates based on extensive numerical studies for approximation along the line using jacobi gauss lobatto quadrature points as the nodal sets are presented the electrostatic analogy is extended to the two dimensional case with the emphasis being on nodal sets inside a triangle for which two very good matrices of nodal sets are presented the matrices are evaluated by computing the lebesgue constants and they share the property that the nodes along the edges of the simplex are the gauss lobatto quadrature points of the chebyshev and legendre polynomials respectively this makes the resulting nodal sets particularly well suited for integration with conventional spectral methods and supplies a new nodal basis for h p finite element methods

a locking free scheme for the lqr control of a timoshenko beam in this paper we analyze a locking free numerical scheme for the lqr control of a timoshenko beam we consider a non conforming finite element discretization of the system dynamics and a control law constant in the spatial dimension to solve the lqr problem we seek a feedback control which depends on the solution of an algebraic riccati equation an optimal error estimate for the feedback operator is proved in the framework of the approximation theory for control of infinite dimensional systems this estimate is valid with constants that do not depend on the thickness of the beam which leads to the conclusion that the method is locking free in order to assess the performance of the method numerical tests are reported and discussed

a high order finite element technique with automatic treatment of stress singularities by semi analytical enrichment abstract this paper presents an approach to the automatic enrichment of finite elements in the vicinity of a stress singularity the enrichment consists of semi analytical singular modes constructed using the scaled boundary finite element method sbfem in contrast to analytical methods the sbfem provides modes for inhomogeneous and anisotropic materials without additional effort the finite element basis can be of arbitrary order and remains unaltered by the enrichment the approach requires enrichment in only one layer of elements around a node due to the compatibility of sbfem with fem there is no need for transitional elements and there are no parasitic terms the approach is tested for several benchmark problems the stress intensity factors are computed based on techniques inspired by the sbfem the proposed procedure is compared to a standard finite element implementation and shows a significant improvement in the error of the displacement field for problems involving singular stresses

a standard test set for numerical approximations to the shallow water equations in spherical geometry a suite of seven test cases is proposed for the evaluation of numerical methods intended for the solution of the shallow water equations in spherical geometry the shallow water equations exhibit the major difficulties associated with the horizontal dynamical aspects of atmospheric modeling on the spherical earth these cases are designed for use in the evaluation of numerical methods proposed for climate modeling and to identify the potential trade offs which must always be made in numerical modeling before a proposed scheme is applied to a full baroclinic atmospheric model it must perform well on these problems in comparison with other currently accepted numerical methods the cases are presented in order of complexity they consist of advection across the poles steady state geostrophically balanced flow of both global and local scales forced nonlinear advection of an isolated low zonal flow impinging on an isolated mountain rossby haurwitz waves and observed atmospheric states one of the cases is also identified as a computer performance algorithm efficiency benchmark for assessing the performance of algorithms adapted to massively parallel computers

information rates for magnetic recording channels with peak and slope limited magnetization a model for magnetic recording is proposed which uses two parameters to describe the limitations on the remanent magnetization in the medium the dimensionless peak value a sub m and the steepest slope b s sup 1 a low pass bandwidth restriction w s sup 1 due to read circuits is also included lower and upper bounds on the achievable transmission rates are derived in terms of the signal to noise ratio for the case of ideal low pass restriction with b

bounds on the information rate of intertransition time restricted binary signaling over an awgn channel upper and lower bounds on the capacity of a continuous time additive white gaussian noise awgn channel with bilevel spl plusmn spl radic p input signals subjected to a minimum inter transition time t sub min constraint are derived the channel model and input constraints reflect basic features of certain magnetic recording systems the upper bounds are based on duncan s relation between the average mutual information in an awgn regime and the mean square error mse of an optimal causal estimator evaluation or upper bounding the mse of suboptimal causal estimators yields the desired upper bounds the lower bound is found by invoking the extended mrs gerber s lemma and asymptotic properties of the entropy of max entropic bipolar d k codes asymptotic results indicate that at low snr pt sub min n sub 0 with n sub 0 designating the noise one sided power spectral density the capacity tends to p n sub 0 nats per second nats s i e it equals the capacity in the simplest average power limited case at high snr the capacity in the simplest average power limited case at high snr the capacity behaves asymptotically as t sub min sup 1 ln snr ln snr nats s demonstrating the degradation relatively to t sub avg sup 1 lnsnr which is the asymptotic known behavior of the capacity with a bilevel average intertransition time t sub avg restricted channel input additional lower bounds are obtained by considering specific signaling formats such as pulsewidth modulation the effect of mild channel filtering on the lower bounds on capacity is also addressed and novel techniques to lower bound the capacity in this case are introduced

necessary and sufficient conditions for the two point phase probability function of two phase random media constructing realizations of random media with a specified two point phase probability function s2 has attracted considerable attention in the recent literature however little is known about cond

on the capacity penalty due to input bandwidth restrictions with an application to rate limited binary signaling it is well known that in cases of unlimited channel bandwidth and unconstrained signal spectrum a constant envelope constraint on the signal does not reduce the capacity of an additive gaussian channel as compared to its capacity with the optimum signals of similar average power for band limited channels of bandwidth b however the constant envelope constraints does reduce the capacity even if the signals themselves are allowed arbitrarily rapid alternations transitions here using a recently introduced technique it is shown that the capacity is further drastically reduced if in addition to the channel limitation the constant envelope signal is itself restricted to a small fractional out of band power epsilon ideal lowpass and bandpass channel filters are considered and upper bounds on the capacity are derived the out of band power restrictions can be met for example by restricting the average rate of transitions rho of the binary input signal it is shown that in this case epsilon

an algorithm for computing fekete points in the triangle on the line and its tensor products fekete points are known to be the gauss lobatto quadrature points but unlike high order quadrature fekete points generalize to non tensor product domains such as the triangle thus fekete points might serve as an alternative to the gauss lobatto points for certain applications in this work we present a new algorithm to compute fekete points and give results up to degree 19 for the triangle for degree d 10 these points have the smallest lebesgue constant currently known the computations validate a conjecture of bos j approx theory 64 1991 pp 271 280 that fekete points along the boundary of the triangle are the one dimensional gauss lobatto points

the scaled boundary finite element method in structural dynamics the scaled boundary finite element method is extended to solve problems of structural dynamics the dynamic stiffness matrix of a bounded finite domain is obtained as a continued fraction solution for the scaled boundary finite element equation the inertial effect at high frequencies is modeled by high order terms of the continued fraction without introducing an internal mesh by using this solution and introducing auxiliary variables the equation of motion of the bounded domain is expressed in high order static stiffness and mass matrices standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain numerical examples for modal and direct time domain analyses are presented rapid convergence is observed as the order of continued fraction increases a guideline for selecting the order of continued fraction is proposed and validated high computational efficiency is demonstrated for problems with stress singularity

scaled boundary polygons for linear elastodynamics abstract a polygonal scaled boundary finite element method sbfem is proposed for linear elastodynamics in two dimensions the domain is divided into non overlapping polygonal elements and the scaled boundary finite element approach is employed over each polygon the advantages are that an arbitrary interpolation order can be used on each polygon and we can choose the optimal element order on each edge individually moreover the sbfem simplifies the numerical integration over the polygons when compared to conventional approaches the dynamic stiffness matrix is computed by employing the continued fraction expansion the influence of the shape of the polygon and the element order on the boundary of each polygon are studied the robustness and the accuracy of the approach are demonstrated with numerical examples

a stochastic scaled boundary finite element method abstract by extending the existing scaled boundary finite element method sbfem into the random field problem a stochastic scaled boundary finite element method ssbfem is developed in this paper to predict the structural responses with randomly distributed material properties the analyzed domain is discretized into a number of polygons modeled as sub domains of the sbfem so that the non homogeneous material properties are possible to be considered in establishment of the constitutive equation the random field represented by the karhunen loeve kl expansion is then directly incorporated into both the equilibrium equation of the sbfem and its sensitivity analysis formulation the perturbation method is employed to calculate the statistical moments of the structural responses and a semi analytical sensitivity analysis method is used to efficiently calculate the gradients involved particularly the proposed method is successfully applied to the stochastic fracture analysis with spatially varying random material properties four numerical examples are investigated to demonstrate the validity of the proposed method

a spectral element semi lagrangian sesl method for the spherical shallow water equations a spectral element semi lagrangian sesl method for the shallow water equations on the sphere is presented the sphere is discretized using a hexahedral grid although any grid imaginable can be used as long as it is comprised of quadrilaterals the equations are written in cartesian coordinates to eliminate the pole singularity which plagues the equations in spherical coordinates in a previous paper int j numer methods fluids 35 2001 869 we showed how to construct an explicit eulerian spectral element se model on the sphere we now extend this work to a semi lagrangian formulation the novelty of the lagrangian formulation presented is that the high order se basis functions are used as the interpolation functions for evaluating the values at the lagrangian departure points this makes the method not only high order accurate but quite general and thus applicable to unstructured grids and portable to distributed memory computers the equations are discretized fully implicitly in time in order to avoid having to interpolate derivatives at departure points by incorporating the coriolis terms into the lagrangian derivative the block lu decomposition of the equations results in a symmetric positive definite pseudo helmholtz operator which we solve using the generalized minimum residual method gmres with a fast projection method comput methods appl mech eng 163 1998 193 results for eight test cases are presented to confirm the accuracy and stability of the method these results show that sesl yields the same accuracy as an eulerian spectral element semi implicit sesi while allowing for time steps 10 times as large and being up to 70 more efficient

consistent infinitesimal finite element cell method three dimensional vector wave equation to calculate the unit impulse response matrix of an unbounded medium for use in a time domain analysis of unbounded medium structure interaction the consistent infinitesimal finite element cell method is developed for the three dimensional vector wave equation this is a boundary finite element procedure the discretization is only performed on the structure medium interface yielding a reduction of the spatial dimension by 1 the procedure is rigorous in the radial direction and exact in the finite element sense in the circumferential directions in contrast to the boundary element procedure the consistent infinitesimal finite element cell method does not require a fundamental solution and incorporates interfaces extending from the structure medium interface to infinity compatible with similarity without any additional computational effort a general anisotropic material can be processed the derivation is based on the finite element formulation and on similarity

a triangular spectral element method applications to the incompressible navier stokes equations abstract encouraged by the success of spectral elements methods in computational fluid dynamics and p type finite element methods in structural mechanics we wish to extend these ideas to solving high order polynomial approximations on triangular domains as the next generation of spectral element solvers we introduce here a complete formulation using a modal basis which has been implemented in a new code ne t r the new basis has the following properties jacobi polynomials of mixed weights semi orthogonality hierarchical structure generalized tensor warped product variable order and a new apex co ordinate system allowing automated integration with gaussian quadrature we have discussed the formulation using a matrix notation which allows for an easy interpretation of the forward and backward transformations we use this notation to formulate the linear advection and helmholtz equations in an efficient manner and show that we recover the following properties well conditioned matrices asymptotic operation count of o n 3 scaling o n 2 of the spectral radius of the weak convective operator and exponential convergence using polynomials up to 40 having constructed and numerically analysed these equations we are then able to solve the incompressible navier stokes equations using a high order splitting scheme we demonstrate a variety of results showing exponential convergence using both deformed and straight triangular subdomains for both the stokes and navier stokes problems

unstructured spectral element methods for simulation of turbulent flows in this paper we present a spectral element fourier algorithm for simulating incompressible turbulent flows in complex geometries using unstructured quadrilateral meshes to this end we compare two different interface formulations for extending the conforming spectral element method in order to allow for surgical mesh refinement and still retain spectral accuracy the zanolli iterative procedure and variational patching based on auxiliary mortar functions we present an interpretation of the original mortar element method as a patching scheme and develop direct and iterative solution techniques that make the method efficient for simulations of turbulent flows the properties of the new method are analyzed in detail by studying the eigenspectra of the advection and diffusion operators we then present numerical results that illustrate the flexibility as well as the exponential convergence of the new algorithm for nonconforming discretizations we conclude with simulation studies of the turbulent cylinder wake at re 1000 external flow and turbulent flow over riblets at re 3280 internal flow

efficient computation of order and mode of three dimensional stress singularities in linear elasticity by the boundary finite element method the boundary finite element method bfem a novel semi analytical boundary element procedure solely relying on standard finite element formulations is employed for the investigation of the orders and modes of three dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates after a comprehensive literature review and a concise introduction to the standard three dimensional bfem formulation for the static analysis of general unbounded structures we demonstrate the application of the bfem for the computation of the orders and modes of two dimensional and three dimensional stress singularities for several classes of problems within the framework of linear elasticity special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates in all cases the bfem computations agree excellently with available reference results the required computational effort is found to be considerably lower compared to e g standard finite element method fem computations in the case of free laminate corners numerous new results on the occurring stress singularities are presented it is found that free corner problems generally seem to involve a more pronounced criticality than the corresponding free edge situations

unsteady analytical solutions of the spherical shallow water equations a new class of unsteady analytical solutions of the spherical shallow water equations sswe is presented analytical solutions of the sswe are fundamental for the validation of barotropic atmospheric models to date only steady state analytical solutions are known from the literature the unsteady analytical solutions of the sswe are derived by applying the transformation method to the transition from a fixed cartesian to a rotating coordinate system fundamental examples of the new unsteady analytical solutions are presented for specific wind profiles with the presented unsteady analytical solutions one can provide a measure of the numerical convergence in the case of a temporally evolving system an application to the atmospheric model plasma shows the benefit of unsteady analytical solutions for the quantification of convergence properties

a parallel adaptive barotropic model of the atmosphere the parallel adaptive model plasma has been developed for modeling a barotropic atmosphere this model adapts the computational grid at every time step according to a physical error indicator thus compared to uniform grid experiments the number of grid points is reduced significantly at the same time the error increases only slightly when comparing with uniform grid solutions for the discretization of the underlying spherical shallow water equations a lagrange galerkin method is used the unstructured triangular grid is maintained by the grid generator amatos and the large linear systems are solved by the parallel solver interface fossi experimental convergence is shown by means of steady state and unsteady analytical solutions plasma yields satisfactory results for quasi standard experiments that is the rossby haurwitz wave and zonal flows over an isolated mountain

efficient wave propagation simulation on quadtree meshes using sbfem with reduced modal basis summary we apply a combination of the transient scaled boundary finite element method sbfem and quadtree based discretization to model dynamic problems at high frequencies we demonstrate that the current formulation of the sbfem for dynamics tends to require more degrees of freedom than a corresponding spectral element discretization when dealing with smooth problems on regular domains thus we improve the efficiency of the sbfem by proposing a novel approach to reduce the number of auxiliary variables for transient analyses based on this improved sbfem we present a modified meshing procedure which creates a quadtree mesh purely based on the geometry and allows arbitrary sizes and orders of elements as well as an arbitrary number of different materials the discretization of each subdomain is created automatically based on material parameters and the highest frequency of interest the transition between regions of different properties is straightforward when using the sbfem the proposed approach is applied to image based analysis with a particular focus on geological models this article is protected by copyright all rights reserved

lagrange galerkin methods on spherical geodesic grids the weak lagrange galerkin finite element method for the 2d shallow water equations on the sphere is presented this method offers stable and accurate solutions because the equations are integrated along the characteristics the equations are written in 3d cartesian conservation form and the domains are discretized using linear triangular elements the use of linear triangular elements permits the construction of accurate by virtue of the second order spatial and temporal accuracies of the scheme and efficient by virtue of the less stringent cfl condition of lagrangian methods schemes on unstructured domains using linear triangles in 3d cartesian space allows for the explicit construction of area coordinate basis functions thereby simplifying the calculation of the finite element integrals the triangular grids are constructed by a generalization of the icosahedral grids that have been typically used in recent papers an efficient searching strategy for the departure points is also presented for these generalized icosahedral grids which involves very few floating point operations in addition a high order scheme for computing the characteristic curves in 3d cartesian space is presented a general family of runge kutta schemes results for six test cases are reported in order to confirm the accuracy of the scheme

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

on filtered binary processes the problem of calculating the probability density function of the output of an rc filter driven by a binary random process with intervals generated by an equilibrium renewal process is studied new integral equations closely related to mcfadden s original integral equations are derived and solved by a matrix approximation method and by iteration transformations of the integral equations into differential equations are investigated and a new closed form solution is obtained in one special case some numerical results that compare the matrix and iteration solutions with both exact solutions and approximate solutions based upon the fokker planck equation are presented

analysis of singular stress fields at multi material corners under thermal loading the scaled boundary finite element method is extended to the modelling of thermal stresses the particular solution for the non homogeneous term caused by thermal loading is expressed as integrals in the radial direction which are evaluated analytically for temperature changes varying as power functions of the radial coordinate when applied to model a multi material corner only the boundary of the problem domain is discretized the boundary conditions on the straight material interfaces and the side faces forming the corner are satisfied analytically without discretization the stress field is expressed semi analytically as a series solution the stress distribution along the radial direction including both the real and complex power singularity and the power logarithmic singularity is represented analytically the stress intensity factors are determined directly from their definitions in stresses no knowledge on asymptotic expansions is required numerical examples are calculated to evaluate the accuracy of the scaled boundary finite element method copyright 2005 john wiley sons ltd

modeling study of a flexible hub beam system with large motion and with considering the effect of shear deformation abstract for a flexible hub beam system with large motion the first order approximation coupling foac model is developed currently which is verified numerically and experimentally to be valid for dynamic description of the system in the foac model the assumption of euler bernoulli beam is adopted with neglecting the effect of shear deformation of flexible beam so this model is only available for the case of slender beam when the beam is short in length direction shear deformation is a factor that may have biggish effect on system dynamics in this paper dynamic modeling of flexible hub beam system with considering the effect of shear deformation is investigated firstly based on the assumption of timoshenko beam and using hamilton s principle a coupling dynamic model with considering shear deformation is established in which geometric stiffness term and axial foreshortening effect caused by the transverse deformation of beam are considered in the modeling subsequently the dynamic model is discretized using finite element method fem finally numerical simulations are carried out to demonstrate the effectiveness of proposed dynamic model simulation results indicate that dynamics characteristics of the hub beam system using the timshenko beam hypothesis and the euler bernoulli beam hypothesis are almost identical when the beam is a slender one for this case shear deformation has little effect on system dynamics but when the beam is short in length direction shear deformation may have biggish effect on system dynamics this effect becomes larger as the width to length ratio increases

unit impulse response of unbounded medium by scaled boundary finite element method to perform a dynamic analysis of a nonlinear structure interacting with an unbounded medium in the time domain it is desirable to formulate the interaction forces of the unbounded medium on the structure medium interface using displacements the corresponding response matrix to a unit impulse of displacements is calculated using the scaled boundary finite element method this method based solely on finite elements is very suitable to model an unbounded medium as the radiation condition at infinity is rigorously satisfied and the discretization is limited to the structure medium interface

diagonalization procedure for scaled boundary finite element method in modeling semi infinite reservoir with uniform cross section to improve the ability of the scaled boundary finite element method sbfem in the dynamic analysis of dam reservoir interaction problems in the time domain a diagonalization procedure was proposed in which the sbfem was used to model the reservoir with uniform cross section first sbfem formulations in the full matrix form in the frequency and time domains were outlined to describe the semi infinite reservoir no sediments and the reservoir bottom absorption were considered second a generalized eigenproblem consisting of coefficient matrices of the sbfem was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors finally using these eigenvalues and eigenvectors to normalize the sbfem formulations yielded diagonal sbfem formulations a diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived an efficient method was presented to evaluate them in this method no riccati equation and lyapunov equations needed solving and no schur decomposition was required which resulted in great computational costs saving the correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains but the diagonalization procedure is only applicable for the sbfem formulation whose scaling center is located at infinity copyright 2009 john wiley sons ltd

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

continued fraction absorbing boundary conditions for convex polygonal domains continued fraction absorbing boundary conditions cfabcs are highly effective boundary conditions for modelling wave absorption into unbounded domains they are based on rational approximation of the exact dispersion relationship and were originally developed for straight computational boundaries in this paper cfabcs are extended to the more general case of polygonal computational domains the key to the current development is the surprising link found between the cfabcs and the complex co ordinate stretching of perfectly matched layers pmls this link facilitates the extension of cfabcs to oblique corners and thus to polygonal domains it is shown that the proposed cfabcs are easy to implement expected to perform better than pmls and are effective for general polygonal computational domains in addition to the derivation of cfabcs a novel explicit time stepping scheme is developed for efficient numerical implementation numerical examples presented in the paper illustrate that effective absorption is attained with a negligible increase in the computational cost for the interior domain although this paper focuses on wave propagation its theoretical development can be easily extended to the more general class of problems where the governing differential equation is second order in space with constant coefficients copyright 2005 john wiley sons ltd

method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces a novel numerical scheme is proposed to solve the shallow water equations swes on arbitrary rotating curved surfaces based on the method of moving frames mmf in which the geometry is represented by orthonormal vectors the proposed scheme not only has the fewest dimensionality both in space and time but also does not require either of metric tensors composite meshes or the ambient space the mmf swe formulation is numerically discretized using the discontinuous galerkin method of arbitrary polynomial order pin space and an explicit runge kutta scheme in time the numerical model is validated against six standard tests on the sphere and the optimal order of convergence of p 1 is numerically demonstrated the mmf swe scheme is also demonstrated for its efficiency and stability on the general rotating surfaces such as ellipsoid irregular and non convex surfaces

higher order triangular spectral element method with optimized cubature points for seismic wavefield modeling the mass lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points known as cubature points to date such points are only known analytically in tensor domains such as quadrilateral or hexahedral elements thus the diagonal mass matrix spectral element method sem in non tensor domains always relies on numerically computed interpolation points or quadrature points however only the cubature points for degrees 1 to 6 are known which is the reason that we have developed a p norm based optimization algorithm to obtain higher order cubature points in this way we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9 the dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration simultaneously the lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties as a result such points provide both good interpolation properties and integration accuracy the courantfriedrichslewy cfl numbers are tabulated for the conventional fekete based triangular spectral element tsem the tsem with exact integration and the optimized cubature based tsem otsem a complementary study demonstrates the spectral convergence of the otsem a numerical example conducted on a half space model demonstrates that the otsem improves the accuracy by approximately one order of magnitude compared to the conventional fekete based tsem in particular the accuracy of the 7th order otsem is even higher than that of the 14th order fekete based tsem furthermore the otsem produces a result that can compete in accuracy with the quadrilateral sem qsem the high accuracy of the otsem is also tested with a non flat topography model in terms of computational efficiency the otsem is more efficient than the fekete based tsem although it is slightly costlier than the qsem when a comparable numerical accuracy is required higher order cubature points for degrees 7 to 9 are developed the effects of quadrature rule on the mass and stiffness matrices has been conducted the cubature points have always positive integration weights freeing from the inversion of a wide bandwidth mass matrix the accuracy of the tsem has been improved in about one order of magnitude

sensitivity analysis of the scaled boundary finite element method for elastostatics abstract as a semi analytical structural analysis algorithm the scaled boundary finite element method sbfem only discretizes the boundary of the analyzed domain without the need of fundamental solutions which makes it powerful for problems with stress singularity or unbounded foundation media in this paper a sensitivity analysis method of sbfem is proposed for elastostatics through which the first order derivatives of the structural responses with respect to the design parameters can be obtained efficiently and accurately an approach is suggested to compute the eigenvalue and eigenvector sensitivities of the hamilton matrix which are then used to calculate the analytical derivative of the stiffness matrix based on these calculations the sensitivities of displacements and stresses are further obtained by a series of differential equations the proposed sensitivity analysis method is also applied to the fracture mechanics problems three numerical examples are investigated to demonstrate the validity of the proposed method

bounds on the symmetric binary cutoff rate for dispersive gaussian channels bounds on the symmetric binary cutoff rate for a pulse amplitude modulated pam signaling over dispersive gaussian channels are evaluated and discussed these easily calculable bounds can be used to estimate the reliable rate of information transmission and the error exponent behavior for binary two level pam schemes operating through a prefiltered additive white gaussian channel the memory of which is long enough to make the exact evaluation of the cutoff rate formidable the core of the bounding technique relies on a probabilistic interpretation of a fundamental theorem in matrix theory regarding the logarithm of the largest eigenvalue of a nonnegative primitive matrix commonly applied in large deviation problems these bounds are calculated for some examples and their respective tightness is considered further potential applications of the proposed bounding technique are pointed out

consistent infinitesimal finite element cell method in plane motion note 189 reference lch article 1995 005 record created on 2007 04 24 modified on 2016 08 08

the stochastic galerkin scaled boundary finite element method on random domain summary the research work extends the scaled boundary finite element method sbfem to non deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random field uncertainties the aim is to blend the sbfem into the galerkin spectral stochastic methods which leads to a proficient procedure for handling the stress singularity problems and crack analysis the young s modulus of structures is considered to have random field uncertainty resulting in the stochastic behaviour of responses mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses displacement strain and stress and stress intensity factors of cracked structures the feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples this article is protected by copyright all rights reserved

a pseudo spectral scheme for the incompressible navier stokes equations using unstructured nodal elements a pseudo spectral scheme for solving the incompressible navier stokes equations using unstructured nodal triangles is proposed efficient algorithms are developed with numerical evidence that indicates optimal rates of convergence can be achieved navier stokes simulations of kovasznay shear layer roll up and row past a cylinder are included to show comparisons between the different nodal sets considered and an alternative modal approach c 2000 academic press

a discontinuous galerkin method for the shallow water equations in spherical triangular coordinates a global model of the atmosphere is presented governed by the shallow water equations and discretized by a runge kutta discontinuous galerkin method on an unstructured triangular grid the shallow water equations on the sphere a two dimensional surface in r 3 are locally represented in terms of spherical triangular coordinates the appropriate local coordinate mappings on triangles on every triangular grid element this leads to a two dimensional representation of tangential momentum and therefore only two discrete momentum equations the discontinuous galerkin method consists of an integral formulation which requires both area elements and line element faces integrals here we use a rusanov numerical flux to resolve the discontinuous fluxes at the element faces a strong stability preserving third order runge kutta method is applied for the time discretization the polynomial space of order k on each curved triangle of the grid is characterized by a lagrange basis and requires high order quadature rules for the integration over elements and element faces for the presented method no mass matrix inversion is necessary except in a preprocessing step the validation of the atmospheric model has been done considering standard tests from williamson et al d l williamson j b drake j j hack r jakob p n swarztrauber a standard test set for numerical approximations to the shallow water equations in spherical geometry j comput phys 102 1992 211 224 unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream a convergence rate of o dx k 1 was observed in the model experiments furthermore a numerical experiment is presented for which the third order time integration method limits the model error thus the time step dt is restricted by both the cfl condition and accuracy demands conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k

lagrange galerkin methods on spherical geodesic grids the shallow water equations abstract the weak lagrange galerkin finite element method for the 2d shallow water equations on the sphere is presented this method offers stable and accurate solutions because the equations are integrated along the characteristics the equations are written in 3d cartesian conservation form and the domains are discretized using linear triangular elements the use of linear triangular elements permits the construction of accurate by virtue of the second order spatial and temporal accuracies of the scheme and efficient by virtue of the less stringent cfl condition of lagrangian methods schemes on unstructured domains using linear triangles in 3d cartesian space allows for the explicit construction of area coordinate basis functions thereby simplifying the calculation of the finite element integrals the triangular grids are constructed by a generalization of the icosahedral grids that have been typically used in recent papers an efficient searching strategy for the departure points is also presented for these generalized icosahedral grids which involves very few floating point operations in addition a high order scheme for computing the characteristic curves in 3d cartesian space is presented a general family of runge kutta schemes results for six test cases are reported in order to confirm the accuracy of the scheme

the scaled boundary finite element method analytical solution in frequency domain the scaled boundary finite element equation a system of ordinary differential equations in the radial coordinate is solved analytically applying a series expansion an eigenvalue problem of a hamiltonian matrix is solved when the difference of two eigenvalues is an even number besides the power series logarithmic functions occur two sets of independent solutions are obtained the scaled boundary finite element method is thus a semi analytical procedure to solve partial differential equations with the polynomial approximation of finite elements in the two circumferential directions and a closed form solution in the radial direction applications to bounded and unbounded domains demonstrate excellent accuracy

a timoshenko beam reduced order model for shape tracking with a slender mechanism abstract we consider a flexible bio inspired slender mechanism modeled as a timoshenko beam it is coupled to the environment by a continuous distribution of compliant elements we derive a reduced order model by projecting the governing partial differential equations along the linear modal basis of the timoshenko beam the coupling with the substrate allows us to formulate the problem in a control framework and eventually to treat the system as a sensor to reconstruct the profile of the substrate through the deformation of the body the coupling is modeled in the framework of two parameters elastic foundations the convergence of the reduced order model with increasing number of basis functions is addressed in a suitable h1 error norm a closed loop force control is simulated for shape morphing when the system is coupled with a smooth substrate

spectral element feti dp and bddc preconditioners with multi element subdomains abstract the discrete systems generated by spectral or hp version finite elements are much more ill conditioned than the ones generated by standard low order finite elements or finite differences this paper focuses on spectral elements based on gauss lobatto legendre gll quadrature and the construction of primal and dual non overlapping domain decomposition methods belonging to the family of balancing domain decomposition methods by constraints bddc and dual primal finite element tearing and interconnecting feti dp algorithms new results are presented for the spectral multi element case and also for inexact feti dp methods for spectral elements in the plane theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator while there is only a polylogarithmic dependence on the spectral degree p and the ratio h h of subdomain and element sizes parallel numerical experiments on a linux cluster confirm these results for tests with spectral degree up to p 32 thousands of subdomains and coefficient jumps up to 8 orders of magnitude

a semi analytical curved element for linear elasticity based on the scaled boundary finite element method summary this work introduces a semi analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method sbfem this approach adapts the fundamental idea of the sbfem concept to scale a boundary to describe a geometry until now scaling in sbfem has exclusively been performed along a straight coordinate that enlarges shrinks or shifts a given boundary in this novel approach scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction the derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures the resulting elements can be coupled to general sbfem or fem domains for elastodynamic problems computations are performed in the frequency domain results of this work are validated using the global matrix method and standard finite element analysis copyright 2016 john wiley sons ltd

isogeometric analysis enhanced by the scaled boundary finite element method abstract by leveraging the information of a typical cad model in the analysis the intensive process of discretization can be circumvented this unification has led to the isogeometric analysis iga hughes et al 2005 however as the cad model provides information only of the boundary a 2d 3d stress analysis is still one major step away in this work the concepts of isogeometric analysis and the scaled boundary finite element method sbfem are combined the sbfem requires only the boundary information and hence provides a seamless integration with the cad modeling within the proposed framework the nurbs basis functions are used to discretize the unknown fields in the circumferential direction whilst analytical solution is sought in the radial direction we further extend the framework to problems with singularities and to dynamic analysis the accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics

achievable rates for a constrained gaussian channel the authors obtained lower bounds to the capacity of the continuous time filtered additive gaussian noise channel with two valued inputs essentially the problem reduces to the continuous time peak limited case which remains an unsolved problem of primary importance in communication theory

a super element for crack analysis in the time domain a super element for the dynamic analysis of two dimensional crack problems is developed based on the scaled boundary finite element method the boundary of the super element containing a crack tip is discretized with lineelements the governing partial differential equations formulated in the scaled boundary co ordinates are transformed to ordinary differential equations in the frequency domain by applying the galerkin s weighted residual technique the displacements in the radial direction from the crack tip to a point on the boundary are solved analytically without any a priori assumption the scaled boundary finite element formulation leads to symmetric static stiffness and mass matrices the super element can be coupled seamlessly with standard finite elements the transient response is evaluated directly in the time domain using a standard time integration scheme the stress field including the singularity around the crack tip is expressed semi analytically the stress intensity factors are evaluated without directly addressing singular functions as the limit in their definitions is performed analytically

a time domain solution for complex multilayered soil model with circular inhomogeneity by the sbfem the scaled boundary finite method sbfem is developed for analyzing wave propagation problem in the two dimensional unbounded domain with rigid bedrock it combines the advantages of the finite element method and boundary element boundary method moreover the original scaling center is replaced by a scaling line which is more suitable for analyzing the multilayered soil model therefore the modified sbfem develops the original sbfem a new derivation of the modified sbfem equation is built in the frame of hamilton system a continued fraction solution of the dynamic stiffness of the soil model with bedrock is obtained for the first time then by introducing the continued fraction solution and auxiliary variables it leads to the model resting on bedrock can be solved in time domain the global equation of motion is solved by the efficient precise time integration method this integral method is firstly employed in the modified sbfem the precision of the proposed method can achieve computer precision therefore an extremely efficient and accurate solution of the modified sbfem in time domain is obtained the results of the complex soil model with circular inhomogeneity show that the proposed method yields excellent results and high accuracy is observed

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

a nodal triangle based spectral element method for the shallow water equations on the sphere a nodal triangle based spectral element se method for the shallow water equations on the sphere is presented the original se method uses quadrilateral elements and high order nodal lagrange polynomials constructed from a tensor product of the legendre gauss lobatto points in this work we construct the high order lagrange polynomials directly on the triangle using nodal sets obtained from the electrostatics principle j s hesthaven from electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex siam journal on numerical analysis 35 1998 655 676 and fekete points m a taylor b a wingate r e vincent an algorithm for computing fekete points in the triangle siam journal on numerical analysis 38 2000 1707 1720 these points have good approximation properties and far better lebesgue constants than any other nodal set derived for the triangle by employing triangular elements as the basic building blocks of the se method and the cartesian coordinate form of the equations we can use any grid imaginable including adaptive unstructured grids results for six test cases are presented to confirm the accuracy and stability of the method the results show that the triangle based se method yields the expected exponential convergence and that it can be more accurate than the quadrilateral based se method even while using 30 60 fewer grid points especially when adaptive grids are used to align the grid with the flow direction however at the moment the quadrilateral based se method is twice as fast as the triangle based se method because the latter does not yield a diagonal mass matrix

a hybrid spectral dg method for solving the phase averaged ocean wave equation algorithm and validation we develop a new high order hybrid discretization of the phased averaged action balance equation to simulate ocean waves we employ discontinuous galerkin dg discretization on an unstructured grid in geophysical space and fourier collocation along the directional and frequency coordinates the original action balance equation is modified to facilitate absorbing boundary conditions along the frequency direction this modification enforces periodicity at the frequency boundaries so that the fast convergence of fourier collocation holds in addition a mapping along the directional coordinate is introduced to cluster the collocation points around steep directional spectra time discretization is accomplished by the tvd runge kutta scheme the overall convergence of the scheme is exponential spectral we successfully verified and validated the method against several analytical solutions observational data and experimental results

the scaled boundary finite element method a fundamental solution less boundary element method in this boundary element method based on finite elements only the boundary is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated and general anisotropic material can be analysed for an unbounded semi infinite or infinite medium the radiation condition at infinity is satisfied exactly no discretization of free and fixed boundaries and interfaces between different materials is required the semi analytical solution inside the domain leads to an efficient procedure to calculate the stress intensity factors accurately without any discretization in the vicinity of the crack tip body loads are included without discretization of the domain thus the scaled boundary finite element method not only combines the advantages of the finite element and boundary element methods but also presents appealing features of its own after discretizing the boundary with finite elements the governing partial differential equations of linear elastodynamics are transformed to the scaled boundary finite element equation in displacement a system of linear second order ordinary differential equations with the radial coordinate as independent variable which can be solved analytically introducing the definition of the dynamic stiffness a system of nonlinear first order ordinary differential equations in dynamic stiffness with the frequency as independent variable is obtained besides the displacements in the interior the static stiffness and mass matrices of a bounded medium and the dynamic stiffness and unit impulse response matrices of an unbounded medium are calculated

high order discontinuous galerkin schemes on general 2d manifolds applied to the shallow water equations an innovating approach is proposed to solve vectorial conservation laws on curved manifolds using the discontinuous galerkin method this new approach combines the advantages of the usual approaches described in the literature the vectorial fields are expressed in a unit non orthogonal local tangent basis derived from the polynomial mapping of curvilinear triangle elements while the convective flux functions are written is the usual 3d cartesian coordinate system the number of vectorial components is therefore minimum and the tangency constraint is naturally ensured while the method remains robust and general since not relying on a particular parametrization of the manifold the discontinuous galerkin method is particularly well suited for this approach since there is no continuity requirement between elements for the tangent basis definition the possible discontinuities of this basis are then taken into account in the riemann solver on inter element interfaces the approach is validated on the sphere using the shallow water equations for computing standard atmospheric benchmarks in particular the williamson test cases are used to analyze the impact of the geometry on the convergence rates for discretization error the propagation of gravity waves is eventually computed on non conventional irregular curved manifolds to illustrate the robustness and generality of the method

a numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method abstract in this paper a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures the formulation is based on the scaled boundary finite element method the through thickness direction of the plate is discretized in the finite element sense while the direction of propagation is described analytically this leads to a standard eigenvalue problem for the calculation of wave numbers the proposed method is not limited to homogeneous plates multi layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation higher order elements have been employed for the finite element discretization leading to excellent convergence for complex structures it is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities

on group fourier analysis and symmetry preserving discretizations of pdes in this paper we review some group theoretic techniques applied to discretizations of pdes inspired by the recent years active research in lie group and exponential time integrators for differential equations we will in the first part of the paper present algorithms for computing matrix exponentials based on fourier transforms on finite groups as an example we consider spherically symmetric pdes where the discretization preserves the 120 symmetries of the icosahedral group this motivates the study of spectral element discretizations based on triangular subdivisions in the second part of the paper we introduce novel applications of multivariate non separable chebyshev polynomials in the construction of spectral element bases on triangular and simplicial sub domains these generalized chebyshev polynomials are intimately connected to the theory of root systems and weyl groups used in the classification of semi simple lie algebras and these polynomials share most of the remarkable properties of the classical chebyshev polynomials such as near optimal lebesgue constants for the interpolation error the existence of fft based algorithms for computing interpolants and pseudo spectral differentiation and existence of gaussian integration rules the two parts of the paper can be read independently

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for diffusion note 264 reference lch article 1999 008doi 10 1002 sici 1097 0207 19990810 45 10 3 0 co 2 eview record in web of science record created on 2007 04 24 modified on 2016 08 08

a matrix function solution for the scaled boundary finite element equation in statics the scaled boundary finite element method is a fundamental solution less boundary element method based on finite elements it leads to semi analytical solutions for displacement and stress fields which permits problems with singularities or in infinite domains to be handled conveniently and accurately however the present eigenvalue method for solving the scaled boundary finite element equation requires additional treatments for multiple eigenvalues with parallel eigenvectors which results from logarithmic terms in the solutions a matrix function solution for the scaled boundary finite element equation in statics is presented in this paper it is numerically stable for multiple or near multiple eigenvalues as it is based on real schur decomposition power functions logarithmic functions and their transitions as occurring in fracture mechanics composites and two dimensional unbounded domains are represented semi analytically no a priori knowledge on the types and orders of singularity are required when simulating stress singularities

the computation of dispersion relations for three dimensional elastic waveguides using the scaled boundary finite element method abstract in this paper a numerical approach for the computation of dispersion relations for three dimensional waveguides with arbitrary cross section is proposed the formulation is based on the scaled boundary finite element method sbfem it is an extension of the approach previously derived for plate structures it is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the z matrix which is well known in the sbfem the hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives the cross section of the waveguide is discretized using higher order spectral elements it is discussed in detail how symmetry axes can be utilized to reduce computational costs in order to sort the solutions at different frequencies a mode tracking algorithm is proposed based on the pade expansion

steady heat conduction analyses using an interpolating element free galerkin scaled boundary method abstract through use of the improved interpolating moving least squares iimls shape functions in the circumferential direction of the scaled boundary method based on the galerkin approach an interpolating element free galerkin scaled boundary method iefg sbm is developed in this paper for analyzing steady heat conduction problems which weakens the governing differential equations in the circumferential direction and seeks analytical solutions in the radial direction the iimls method exhibits some advantages over the moving least squares approximation and the interpolating moving least squares method because its shape functions possess the delta function property and the involved weight function is nonsingular in the iefg sbm only a nodal data structure on the boundary is required and the primary unknown quantities are real solutions of nodal variables higher accuracy and faster convergence are obtained due to the increased smoothness and continuity of shape functions based on the iefg sbm the steady heat conduction problems with thermal singularities and unbounded domains can be ideally modeled some numerical examples are presented to validate the availability and accuracy of the present method for steady heat conduction analysis

unit impulse response matrix of unbounded medium by finite element based forecasting note 172 reference lch article 1995 003doi 10 1002 nme 1620380702 record created on 2007 04 24 modified on 2016 08 08

a modified scaled boundary finite element method for three dimensional dynamic soil structure interaction in layered soil summary this paper is devoted to the analysis of elastodynamic problems in 3d layered systems which are unbounded in the horizontal direction for this purpose a finite element model of the near field is coupled to a scaled boundary finite element model sbfem of the far field the sbfem is originally based on describing the geometry of a half space or full space domain by scaling the geometry of the near field far field interface using a radial coordinate a modified form of the sbfem for waves in a 2d layer is also available none of these existing formulations can be used to describe a 3d layered medium in this paper a modified sbfem for the analysis of 3d layered continua is derived based on the use of a scaling line instead of a scaling centre a suitable scaled boundary transformation is proposed the derivation of the corresponding scaled boundary finite element sbfe equations in displacement and stiffness is presented in detail the latter is a nonlinear differential equation with respect to the radial coordinate which has to be solved numerically for each excitation frequency considered in the analysis various numerical examples demonstrate the accuracy of the new method and its correct implementation these include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3d soil deposits over rigid bedrock hysteretic damping is assumed in some cases the dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results copyright 2011 john wiley sons ltd

upper bounds on capacity for a constrained gaussian channel a low pass and a bandpass additive white gaussian noise channel with a peak power constraint imposed on otherwise arbitrary input signals are considered upper bounds on the capacity of such channels are derived they are strictly less than the capacity of the channel when the peak power constrain is removed and replaced by the average power constraint for which the gaussian inputs are optimum this provides the answer to an often posed question peak power limiting in the case of bandlimited channels does reduce capacity whereas in infinite bandwidth channels it does not as is well known for an ideal low pass filter of bandwidth b the upper bound is blog 0 934p n sub 0 b for p n sub 0 b 1 where p is the peak power of the input signal and n sub 0 2 is the double sided power spectral density of the additive white gaussian noise

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

investigation of a two dimensional spectral element method for helmholtz s equation a spectral element method is developed for solving the two dimensional helmholtz s equation which is the equation governing time harmonic acoustic waves computational cost for solving helmholtz s equation with the galerkin finite element method increases as the wave number increases due to the pollution effect therefore a more efficient numerical method is sought the comparison between a spectral element method and a second order finite element method shows that the spectral element method leads to fewer grid points per wavelength and less computational cost for the same accuracy it also offers the same advantage as the finite element method to address complex geometry and general material property some simple examples are addressed and compared with the exact solutions to confirm the accuracy of the method for unbounded problems the symmetric perfectly matched layer pml method is applied to treat the non reflecting boundary conditions in the pml method a fictitious absorbing layer is introduced outside the truncated boundary

a hybrid meshless local petrov galerkin method for unbounded domains abstract meshless methods have gained popularity in recent years however like the finite element method they do not handle unbounded domains well coupling with other techniques more suited to performing this task is problematic since nodal values on the boundary are fictitious rather than actual the scaled boundary finite element method is a semi analytical approach to computational mechanics ideally suited to modelling unbounded domains recently a meshless version of the scaled boundary method based on the local petrov galerkin approach has been developed this paper couples the meshless scaled boundary method used to model the far field with conventional meshless local petrov galerkin modelling of the near field the coupling method is general and could be applied to other techniques of modelling the far field such as the infinite element method

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