a numerical continuation method based on pade approximants a continuation algorithm is presented with a new predictor which is based on a rational representation of the solution path this algorithm belongs to the class of asymptotic numerical methods that connect perturbation techniques with a discretization principle without the use of a correction process several examples from shell buckling and from contact mechanics are analyzed to assess the efficiency and the reliability of the method

quasi newton methods for implicit black box fsi coupling abstract in this paper we introduce a new multi vector update quasi newton mvqn method for implicit coupling of partitioned transient fsi solvers the new quasi newton method facilitates the use of black box field solvers and under certain circumstances can be demonstrated to provide newton like convergence behaviour for strongly coupled fsi benchmark problems we demonstrate the superior convergence behaviour and robust nature of the mvqn method compared to other well known quasi newton coupling schemes including the least squares reduced order modelling ibqn ls scheme the classical rank 1 update broyden s method and fixed point iterations with dynamic relaxation the quasi newton methods are analysed on a suite of strongly coupled fsi problems including but not limited to internal incompressible flow through a flexible tube where the solid density is an order of magnitude lower than the fluid density

numerical comparisons of high order nonlinear solvers for the transient navier stokes equations based on homotopy and perturbation techniques efficient solvers for the unsteady navier stokes equations are presented a classic time stepping scheme is combined with high order nonlinear solvers coupling homotopy and a perturbation technique polynomial and rational representations are used to approximate the unknowns of the problem a pseudo residual criterion is proposed to improve the efficiency of the solvers the numerical example considered in this paper is the time periodic two dimensional flow around a circular cylinder comparisons with the classical first order newton raphson solver are performed numerical results reveal that a lower number of matrix factorization is needed with the proposed methods decreasing the computational effort

model order reduction in hyperelasticity a proper generalized decomposition approach this paper deals with the extension of proper generalized decomposition methods to non linear problems in particular to hyperelasticity among the different approaches that can be considered for the linearization of the doubly weak form of the problem we have implemented a new one that uses asymptotic numerical methods in conjunction with proper generalized decomposition to avoid complex consistent linearization schemes necessary in newton strategies this approach results in an approximation of the problem solution in the form of a series expansion each term of the series is expressed as a finite sum of separated functions the advantage of this approach is the presence of only one tangent operator identical for every term in the series the resulting approach has proved to render very accurate results that can be stored in the form of a meta model in a very compact format this opens the possibility to use these results in real time reaching khz feedback rates or to be used in deployed handheld devices such as smartphones and tablets

incompressible flow past a circular cylinder dependence of the computed flow field on the location of the lateral boundaries the influence of the location of the lateral boundaries on 2d computation of unsteady incompressible flow past a circular cylinder is investigated the case of reynolds number 100 is used as a benchmark and several quantities characterizing the unsteady flow are obtained for a range of lateral boundary locations the computations are performed with two distinct finite element formulations space time velocity pressure formulation and velocity pressure stress formulation we conclude that the distance between the cylinder and the lateral boundaries can have a significant effect on the strouhal number and other flow quantities the minimum distance at which this influence vanishes has been found to be larger than what is commonly assumed

infinite toeplitz and laurent matrices with localized impurities this paper is concerned with the change of the spectra of infinite toeplitz and laurent matrices under perturbations in a prescribed finite set of sites the main result says that the spectrum of a toeplitz matrix with a non constant rational symbol is not affected by small localized impurities while such impurities can nevertheless enlarge the spectrum of the corresponding laurent matrix we also study the spectra that may emerge when randomly perturbing toeplitz or laurent matrices in a randomly chosen single site

analysis and application of high order implicit runge kutta schemes for unsteady conjugate heat transfer a strongly coupled approach abstract thermal interaction of fluids and solids or conjugate heat transfer cht is encountered in many engineering applications since time accurate computations of unsteady cht can be computationally demanding we consider the use of high order implicit time integration schemes which have the potential to be more efficient relative to the commonly used second order implicit schemes we present a strongly coupled solution algorithm where the high order l stable explicit first stage singly diagonally implicit runge kutta esdirk schemes are used to advance the solution in time within each separate fluid and solid subdomains furthermore the stability and rate of convergence of performing gauss seidel subiterations at each stage of the esdirk schemes are analyzed the results from solving a numerical example an unsteady conjugate natural convection in an enclosure show good agreement with the performed analytical stability analysis in addition the computational work temporal precision character of several schemes in solving a strongly coupled cht problem is compared over a range of accuracy requirements from the efficiency investigation it is observed that performing subiterations with the strongly coupled esdirk algorithm is more efficient than lowering time step size using a high order loosely coupled imex algorithm in addition by using the esdirk schemes gain in computational efficiency relative to crank nicolson is observed for time accurate solutions a factor of 1 4 using the fourth order esdirk the computational gain is higher for smaller tolerances

optimized strong stability preserving imex runge kutta methods we construct and analyze robust strong stability preserving implicit explicit runge kutta imex rk methods for models of flow with diffusion as they appear in astrophysics and in many other fields where equations with similar structure arise it turns out that besides the optimization of the region of absolute monotonicity some other properties of the methods are crucial for the success of such simulations in particular the models in our focus dictate to also take into account the step size limits associated with dissipativity positivity of the stiff parabolic terms which represent transport by diffusion the uniform convergence with respect to different stiffness properties of those same terms etc furthermore in the literature some other properties like the inclusion of a part of the imaginary axis in the stability region have been argued to be relevant in this paper we construct several new imex rk methods which differ from each other by taking various or even all of these constraints simultaneously into account it is demonstrated for some simple examples as well as for the problem of double diffusive convection that the newly constructed schemes provide a significant computational advantage over other methods from the literature due to their accumulation of different stability properties the optimized imex rk methods obtained in this paper are robust schemes that may also be useful for general models which involve the solution of advection diffusion equations or other transport equations with similar stability requirements

comparison between lattice boltzmann method and navier stokes high order schemes for computational aeroacoustics computational aeroacoustic caa simulation requires accurate schemes to capture the dynamics of acoustic fluctuations which are weak compared with aerodynamic ones in this paper two kinds of schemes are studied and compared the classical approach based on high order schemes for navier stokes like equations and the lattice boltzmann method the reference macroscopic equations are the 3d isothermal and compressible navier stokes equations a von neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions three physical modes are recovered and the corresponding theoretical dispersion relations are obtained then the same analysis is made on the space and time discretization of the navier stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions different orders of discretization are considered with and without a uniform mean flow three different lattice boltzmann models are then presented and studied with the von neumann analysis the theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied it is shown that the dispersion error in the lattice boltzmann models is only due to the space and time discretization and that the continuous discrete velocity boltzmann equation yield the same exact dispersion as the navier stokes equations finally dispersion and dissipation errors of the different kind of schemes are quantitatively compared it is found that the lattice boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3 step runge kutta scheme in time the number of floating point operations at a given error level associated with these two kinds of schemes are then compared

time integration algorithm based on divergent series resummation for ordinary and partial differential equations borel s technique of divergent series resummation is transformed into a numerical code and used as a time integration scheme it is applied to the resolution of regular and singular problems arising in fluid mechanics its efficiency is compared to those of classical discretization schemes

high order prediction correction algorithms for unilateral contact problems in this paper high order prediction correction algorithms are presented to solve unilateral contact problems these algorithms are built up using the asymptotic numerical method which associates a perturbation technique with a numerical one as the finite element method

automatic detection and branch switching methods for steady bifurcation in fluid mechanics this paper deals with the computation of steady bifurcations in the framework of 2d incompressible navier stokes flow we first propose a numerical method to accurately detect the critical reynolds number where this kind of bifurcation appears from this singular value we introduce a numerical tool to compute all the steady bifurcated branches all these algorithms are based on the asymptotic numerical method 1 2 the critical values are determined by using a bifurcation indicator 3 5 and the bifurcated branches are computed by using an augmented system which was first introduced in solid mechanics 4 6 several numerical examples from 2d navier stokes show the reliability and the efficiency of the proposed methods

high order explicit local time stepping methods for damped wave equations locally refined meshes impose severe stability constraints on explicit time stepping methods for the numerical simulation of time dependent wave phenomena local time stepping methods overcome that bottleneck by using smaller time steps precisely where the smallest elements in the mesh are located starting from classical adams bashforth multi step methods local time stepping methods of arbitrarily high order of accuracy are derived for damped wave equations when combined with a finite element discretization in space with an essentially diagonal mass matrix the resulting time marching schemes are fully explicit and thus inherently parallel numerical experiments with continuous and discontinuous galerkin finite element discretizations corroborate the expected rates of convergence and illustrate the usefulness of these local time stepping methods

spectra pseudospectra and localization for random bidiagonal matrices there has been much recent interest initiated by work of the physicists hatano and nelson in the eigenvalues of certain random non hermitian periodic tridiagonal matrices and their bidiagonal limits these eigenvalues cluster along a bubble with wings in the complex plane and the corresponding eigenvectors are localized in the wings delocalized in the bubble here in addition to eigenvalues pseudospectra are analyzed making it possible to treat the nonperiodic analogues of these random matrix problems inside the bubble the resolvent norm grows exponentially with the dimension outside it grows subexponentially in a bounded region that is the spectrum of the infinite dimensional operator localization and delocalization correspond to resolvent matrices whose entries exponentially decrease or increase respectively with distance from the diagonal this article presents theorems that characterize the spectra pseudospectra and numerical range for the four cases of finite bidiagonal matrices infinite bidiagonal matrices stochastic toeplitz operators finite periodic matrices and doubly infinite bidiagonal matrices stochastic laurent operators c 2001 john wiley sons inc

an iterative process based on homotopy and perturbation techniques abstract in this paper we discuss high order iterative methods whose principle has been presented recently n damil m potier ferry a najah r chari r lahmam communications in numerical methods in engineering 15 1999 701 708 these algorithms are optimised by appropriate choices of the homotopy transformation of the perturbation technique and of the strategy of control especially the use of pade approximants yields very efficient algorithms as compared with classical first order ones a classical non linear elastic shell problem permits us to assess the efficiency of the proposed method

a study of the eigenvalue sensitivity by homotopy and perturbation methods in this work the sensitivity to material characteristics of eigenvalues is studied from an initial structure some defects of material or and geometry are introduced a method is proposed to solve the new eigenvalue problem from the initial one without using classical techniques this method is based on the association of a homotopy transformation and the perturbation method

compact fourth order finite volume method for numerical solutions of navier stokes equations on staggered grids the development of a compact fourth order finite volume method for solutions of the navier stokes equations on staggered grids is presented a special attention is given to the conservation laws on momentum control volumes a higher order divergence free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes three forms of the nonlinear correction for staggered grids are proposed and studied the accuracy of each approximation is assessed comparatively in fourier space the importance of higher order approximations of pressure is discussed and numerically demonstrated fourth order accuracy of the complete scheme is illustrated by the doubly periodic shear layer and the instability of plane channel flow the efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations the proposed scheme is highly accurate and efficient at the same level of accuracy the fourth order scheme can be ten times faster than the second order counterpart this gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost

stabilized stress velocity pressure finite element formulations of the navier stokes problem for fluids with non linear viscosity abstract the three field stress velocity pressure mixed formulation of the incompressible navier stokes problem can lead to two different types of numerical instabilities the first is associated with the incompressibility and loss of stability in the calculation of the stress field and the second with the dominant convection the first type of instabilities can be overcome by choosing an interpolation for the unknowns that satisfies the appropriate inf sup conditions whereas the dominant convection requires a stabilized formulation in any case this paper proposes two stabilized schemes of sub grid scale sgs type differing in the definition of the space of the sub grid scales and both allowing to use the same interpolation for the variables u p deviatoric stress velocity and pressure even in problems where the convection component is dominant and the velocity stress gradients are high another aspect considered in this work is the non linearity of the viscosity modeled with constitutive models of quasi newtonian type this paper includes a description of the proposed methods some of their implementation issues and a discussion about benefits and drawbacks of a three field formulation several numerical examples serve to justify our claims

spectral properties of random non self adjoint matrices and operators i describe some numerical experiments which determine the degree of spectral instability of medium sized randomly generated matrices which are far from self adjoint the conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size i also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the eigenvectors generate a dense linear subspace but the eigenvalues do not determine the spectrum my results imply that the spectrum of the non self adjoint anderson model changes suddenly on passing to the infinite volume limit

non hermitian localization and delocalization we study localization and delocalization in a class of non hermitian hamiltonians inspired by the problem of vortex pinning in superconductors in various simplified models we are able to obtain analytic descriptions in particular of the nonperturbative emergence of a forked structure the appearance of wings in the density of states we calculate how the localization length diverges at the localization delocalization transition we map some versions of this problem onto a random walker problem in two dimensions for a certain model we find an intricate structure in its density of states

the asymptotic spectra of banded toeplitz and quasi toeplitz matrices toeplitz matrices occur in many mathematical as well as scientific and engineering investigations this paper considers the spectra of banded toeplitz and quasi toeplitz matrices with emphasis on n

power series analysis as a major breakthrough to improve the efficiency of asymptotic numerical method in the vicinity of bifurcations this paper presents the outcome of power series analysis in the framework of the asymptotic numerical method we theoretically demonstrate and numerically evidence that the emergence of geometric power series in the vicinity of simple bifurcation points is a generic behavior so we propose to use this hallmark as a bifurcation indicator to locate and compute very efficiently any simple bifurcation point finally a power series that recovers an optimal step length is build in the neighborhood of bifurcation points the reliability and robustness of this powerful approach is then demonstrated on two application examples from structural mechanics and hydrodynamics