efficient arnoldi type algorithms for rational eigenvalue problems arising in fluid solid systems we develop and analyze efficient methods for computing damped vibration modes of an acoustic fluid confined in a cavity with absorbing walls capable of dissipating acoustic energy the discretization in terms of pressure nodal finite elements gives rise to a rational eigenvalue problem numerical evidence shows that there are no spurious eigenmodes for such discretization and also confirms that the discretization based on nodal pressures is much more efficient than that based on raviart thomas finite elements for the displacement field the trimmed linearization method is used to linearize the associated rational eigenvalue problem into a generalized eigenvalue problem gep of the form ax lbx for solving the gep we apply arnoldi algorithm to two different types of single matrices b 1a and ab 1 numerical accuracy shows that the application of arnoldi on ab 1 is better than that on b 1a

a hexahedral face element for elastoacoustic vibration problems a finite element method to compute elastoacoustic vibration modes in 3d problems is analyzed it is based on displacement formulations for solid and fluid the discretization consists of classical isoparametric hexahedral elements for the former and hexahedral raviart thomas elements for the latter to avoid spurious modes the meshes on fluid and solid domains do not need to coincide on the common interface since the kinematic constraint is weakly imposed the generalized eigenvalue problem is written in a matrix form which allows using a standard matlab eigensolver numerical results showing the good performance of the method and the convenience of using incompatible meshes are reported

a smoothed coupled ns nes fem for dynamic analysis of 2d fluid solid interaction problems abstract a node based smoothed finite element method ns fem t3 using triangular elements and a n sided polygonal edge based smoothed fem n es fem using polygonal elements is combined to give the smoothed coupled ns n es fem for dynamic analysis of two dimensional 2d fluid solid interaction problems based on the pressure displacement formulation in the present method the ns fem t3 is used for the fluid domain and the gradient of pressure is smoothed while the n es fem is used for the solid domain and the gradient of displacement is smoothed this gradient smoothing technique can provide proper softening effect which will effectively relieve the overly stiff behavior of the fem model and thus improve significantly the solution of coupled system some numerical examples have been presented to illustrate the effectiveness of the coupled ns n es fem compared with some existing methods for 2d fluid solid interaction problems

discontinuous galerkin methods with plane waves for the displacement based acoustic equation several special finite element methods have been proposed to solve helmholtz problems in the mid frequency regime such as the partition of unity method the ultra weak variational formulation and the discontinuous enrichment method the first main purpose of this paper is to present a discontinuous galerkin method with plane waves which is a variant of the discontinuous enrichment method to solve the displacement based acoustic equation the use of the displacement variable is often necessary in the context of fluid structure interactions a well known issue with this model is the presence of spurious vortical modes when one uses standard finite elements such as lagrange elements this problem also known as the locking phenomenon is observed with several other vector based equations such as incompressible elasticity and electromagnetism so this paper also aims at assessing if the special finite element methods suffer from the locking phenomenon in the context of the displacement acoustic equation the discontinuous galerkin method presented in this paper is shown to be very accurate and stable i e no spurious modes are observed the optimal choice of the various parameters are discussed with regards to numerical accuracy and conditioning some interesting properties of the mixed displacement pressure formulation are also presented furthermore the use of the partition of unity method is also presented but it is found that spurious vortical modes may appear with this method

super convergence and post processing for mixed finite element approximations of the wave equation we consider the numerical approximation of acoustic wave propagation problems by mixed text bdm k 1 text p k finite elements on unstructured meshes optimal convergence of the discrete velocity and super convergence of the pressure are established based on these results we propose a post processing strategy that allows us to construct an improved pressure approximation from the numerical solution corresponding results are well known for mixed finite element approximations of elliptic problems and we extend these analyses here to the hyperbolic problem under consideration we also consider the subsequent time discretization by the crank nicolson method and show that the analysis and the post processing strategy can be generalized to the fully discrete schemes our proofs do not rely on duality arguments or inverse inequalities and the results therefore also apply for non convex domains and non uniform meshes

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

trapping of random walks on small world networks we investigate the trapping of random walkers on small world networks swn s irregular graphs we derive bounds for the survival probability phi swn n and display its analysis through cumulant expansions computer simulations are performed for large swns we show that in the limit of infinite sizes trapping on swns is equivalent to trapping on a certain class of random trees which are grown during the random walk

stability and accuracy of finite element methods for flow acoustics i general theory and application to one dimensional propagation the dispersion properties of finite element models for aeroacoustic propagation based on the convected scalar helmholtz equation and on the galbrun equation are examined the current study focusses on the effect of the mean flow on the dispersion and amplitude errors present in the discrete numerical solutions a general two dimensional dispersion analysis is presented for the discrete problem on a regular unbounded mesh and results are presented for the particular case of one dimensional acoustic propagation in which the wave direction is aligned with the mean flow the magnitude and sign of the mean flow is shown to have a significant effect on the accuracy of the numerical schemes quadratic helmholtz elements in particular are shown to be much less effective for downstream as opposed to upstream propagation even when the effect of wave shortening or elongation due to the mean flow is taken into account these trends are also observed in solutions obtained for simple test problems on finite meshes a similar analysis of two dimensional propagation is presented in an accompanying article

finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics a quadratic eigenvalue problem arising in the determination of the vibration modes of an acoustic fluid contained in a cavity with absorbing walls is considered the problem is shown to be equivalent to the spectral problem for a noncompact operator and a thorough spectral characterization is given a numerical discretization based on raviart thomas finite elements is analyzed the method is proved to be free of spurious modes and to converge with optimal order implementation issues and numerical experiments confirming the theoretical results are reported

search in power law networks many communication and social networks have power law link distributions containing a few nodes that have a very high degree and many with low degree the high connectivity nodes play the important role of hubs in communication and networking a fact that can be exploited when designing efficient search algorithms we introduce a number of local search strategies that utilize high degree nodes in power law graphs and that have costs scaling sublinearly with the size of the graph we also demonstrate the utility of these strategies on the gnutella peer to peer network

a coupled alpha fem for dynamic analyses of 2d fluid solid interaction problems abstract an alpha finite element method using triangular elements fem t3 which combines the node based smoothed fem ns fem t3 and standard fem t3 with a scale factor 0 1 is extended to the dynamic analysis of 2d fluid solid interaction problems based on the pressure displacement formulation the gradient smoothing technique based on a part of the smoothing domains associated with the nodes of the triangles is used to smooth both the gradient of pressure and gradient of displacement this gradient smoothing technique can provide proper softening effect and thus improve significantly the accuracy of solution of coupled system some numerical examples have been presented to illustrate the effectiveness and stability of the fem t3 0 6 compared with some existing methods for 2d fluid solid interaction problems

topology optimization of acoustic structure interaction problems using a mixed finite element formulation the paper presents a gradient based topology optimization formulation that allows to solve acoustic structure vibro acoustic interaction problems without explicit boundary interface representation in acoustic structure interaction problems the pressure and displacement fields are governed by helmholtz equation and the elasticity equation respectively normally the two separate fields are coupled by surface coupling integrals however such a formulation does not allow for free material re distribution in connection with topology optimization schemes since the boundaries are not explicitly given during the optimization process in this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables a u p formulation the helmholtz equation is obtained as a special case of the mixed formulation for the elastic shear modulus equating to zero hence by spatial variation of the mass density shear and bulk moduli we are able to solve the coupled problem by the mixed formulation using this modelling approach the topology optimization procedure is simply implemented as a standard density approach several two dimensional acoustic structure problems are optimized in order to verify the proposed method copyright 2006 john wiley sons ltd

an efficient and high order frequency domain approach for transient acoustic structure interactions in three dimensions this paper is concerned with numerical solution of the transient acoustic structure interaction problems in three dimensions an efficient and higher order method is proposed with a combination of the exponential window technique and a fast and accurate boundary integral equation solver in the frequency domain the exponential window applied to the acoustic structure system yields an artificial damping to the system which eliminates the wrap around errors brought by the discrete fourier transform the frequency domain boundary integral equation approach relies on accurate evaluations of relevant singular integrals and fast computation of nonsingular integrals via the method of equivalent source representations and the fast fourier transform numerical studies are presented to demonstrate the accuracy and efficiency of the method copyright 2016 john wiley sons ltd

on a method for vibration analysis of viscous compressible fluid structure systems a fluid structure interaction formulation for viscous compressible fluid is under consideration the formulation involves finite element approximation of linearized navier stokes equations and response determination made by means of modal superposition analysis standard and simplified schemes of the viscous compressible fluid structure interaction problem solution are developed the schemes are based on the frequency condensation method of a complex eigenvalue problem solving free and forced oscillations of several fluid structure systems are studied by the standard and simplified schemes the analysis of the results obtained shows that the simplified scheme provides a saving of 90 of the computational time required to define oscillation of the structure with viscous compressible fluid in the lowest frequency range a certain influence of the fluid viscosity on the transient response of the fluid structure system is also demonstrated copyright 2004 john wiley sons ltd

approximate selections fixed points almost fixed points of multivalued mapping and generalized quasi variational inequalities in h spaces a fixed point theorem for continuous multivalued mapping with closed h convex values is analyzed using the almost fixed point theorem new approximate selection theorems a new almost fixed point theorem for a lower semicontinuous multivalued mapping and a new existence theorem for solutions of a generalized quasi variational inequality in h spaces are discussed

numerical solution of the acoustic wave equation using raviart thomas elements in this paper we discuss the numerical approximation of the displacement form of the acoustic wave equation using mixed finite elements the mixed formulation allows for approximation of both displacement and pressure at each time step without the need for post processing lowest order and next to lowest order raviart thomas elements are used for the spatial discretization and centered finite differences are used to advance in time use of these raviart thomas elements results in a diagonal mass matrix for resolution of pressure and a mass matrix for the displacement variable that is sparse with a simple structure convergence results for a model problem are provided as are numerical results for a two dimensional problem with a point source

behaviour of isoparametric quadrilateral family of lagrangian fluid finite elements this paper presents the formulation of both the consistent and inconsistent four eight and nine noded isoparametric quadrilateral fluid finite elements that are based on lagrangian frame of reference the mesh locking phenomenon due to simultaneous enforcement of twin constraints namely the incompressibility and irrotationality constraints is studied in detail the study shows that the characteristic of the locked fluid elements is that it always generates numerous spurious acoustic volume change modes upon the enforcement of rotational constraints that is the rotational constraints change the character of certain volume change modes the study further reinforces the necessity of rotational constraints in not only identifying the spurious pressure modes but also in reducing the computational effort for determining the eigenvalues and eigenvectors it is found that all fully integrated inconsistent models exhibit locking behaviour however the inconsistent eight and nine noded elements integrated with full integration of volumetric stiffness and one point integration of the rotational stiffness matrices gives excellent performance although they do not pass the inf sup test the four and nine noded consistent models are found to give locking free performance while their eight noded counterpart exhibited locking behaviour the study shows that only consistent nine noded element models pass the inf sup test the utility of these elements in coupled fluid structure interaction problem is also demonstrated

displacement pressure based mixed finite element formulations for acoustic fluid structure interaction problems summary we present reliable finite element discretizations based on displacement pressure interpolations for the analysis of acoustic fluid structure interaction problems the finite element interpolations are selected using the inf sup condition and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation we show that with our analysis procedure no spurious non zero frequencies are encountered as heretofore calculated with other displacement based discretizations 1997 by john wiley sons ltd

kinetic growth walks on complex networks kinetically grown self avoiding walks on various types of generalized random networks have been studied networks with short and long tailed degree distributions p k were considered k degree or connectivity including scale free networks with p k k the long range behaviour of self avoiding walks on random networks is found to be determined by finite size effects the mean self intersection length of non reversal random walks l scales as a power of the system size n l n with an exponent 0 5 for short tailed degree distributions and 0 5 for scale free networks with 3 the mean attrition length of kinetic growth walks l scales as l n with an exponent which depends on the lowest degree in the network results of approximate probabilistic calculations are supported by those derived from simulations of various kinds of networks the efficiency of kinetic growth walks to explore networks is largely reduced by inhomogeneity in the degree distribution as happens for scale free networks

topology optimization for acoustic structure interaction problems we propose a gradient based topology optimization algorithm for acoustic structure vibro acoustic interaction problems without an explicit interfacing boundary representation in acoustic structure interaction problems the pressure field and the displacement field are governed by the helmholtz equation and the linear elasticity equation respectively and it is necessary that the governing equations should be properly evolved with respect to the design variables in the design domain moreover all the boundary conditions obtained by computing surface coupling integrals should be properly imposed to subdomain interfaces evolving during the optimization process in this paper we propose to use a mixed finite element formulation with displacements and pressure as primary variables u p formulation which eliminates the need for explicit boundary representation in order to describe the helmholtz equation and the linear elasticity equation the mass density as well as the shear and bulk moduli are interpolated with the design variables in this formulation the coupled interface boundary conditions are automatically satisfied without having to compute surface coupling integrals two dimensional acoustic structure interaction problems are optimized to show the validity of the proposed method

vibration analysis of fluid solid systems using a finite element displacement formulation this report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid the equation of motion governing the inviscid fluid is expressed in terms of the displacements reduced integration is used when computing the element stiffness matrix contributed by the fluid in addition a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration

collapse transition and crossover scaling for self avoiding walks on the diamond lattice a monte carlo study of self avoiding walks on the diamond lattice is presented this model incorporates some of the steric effects and short range stiffness of real alkanes and for a nearest neighbour attractive interaction epsilon is found to have a collapse transition at kb theta epsilon 2 25 or 0 05 the behaviour of the chains in the vicinity of this theta temperature is analysed with the help of recent crossover scaling theories it is shown that for finite chain length n there is a rather broad theta region where the chains behaviour is quasi ideal the width of this region wtheta behaves as omega 0 varies as n 12 consistent with the blob picture the peak of the specific heat occurs at the boundary between the theta region and the region of collapsed chains the authors also give rough estimates for the scaling functions describing the crossovers of the end to end distance and structure factor of the chains

on computational issues of immersed finite element methods the objective of this paper is to provide a review of recent finite element formulations for immersed methods in these finite element formulations independent lagrangian solid meshes are introduced to move on top of a background eulerian fluid mesh this key feature allows the handling without excessive fluid mesh adaptation multiple deformable solids immersed in viscous fluid in particular pros and cons of both explicit and implicit approaches are illustrated along with subtle differences between incompressible and slightly compressible models

a mixed finite element method for acoustic wave propagation in moving fluids based on an eulerian lagrangian description a nonstandard wave equation established by galbrun in 1931 is used to study sound propagation in nonuniform flows galbrun s equation describes exactly the same physical phenomenon as the linearized euler s equations lee but is derived from an eulerian lagrangian description and written only in term of the lagrangian perturbation of the displacement this equation has interesting properties and may be a good alternative to the lee only acoustic displacement is involved even in nonhomentropic cases it provides exact expressions of acoustic intensity and energy and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly in this paper galbrun s equation is solved using a finite element method in the axisymmetric case with standard finite elements the direct displacement based variational formulation gives some corrupted results instead a mixed finite element satisfying the inf sup condition is proposed to avoid this problem a first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow obtained from pridmore brown s equation a second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple scale method which is an adaptation for the incompressible case of rienstra s recent work

finite element approximation of spectral acoustic problems on curved domains this paper deals with the finite element approximation of the displacement formulation of the spectral acoustic problem on a curved non convex two dimensional domain convergence and error estimates are proved for raviart thomas elements on a discrete polygonal domain h inline equation in the framework of the abstract spectral approximation theory similar results have been previously proved only for polygonal domains numerical tests confirming the theoretical results are reported

time harmonic solution for acousto elastic interaction with controllability and spectral elements the classical way of solving the time harmonic linear acousto elastic wave problem is to discretize the equations with finite elements or finite differences this approach leads to large scale indefinite complex valued linear systems for these kinds of systems it is difficult to construct efficient iterative solution methods that is why we use an alternative approach and solve the time harmonic problem by controlling the solution of the corresponding time dependent wave equation in this paper we use an unsymmetric formulation where fluid structure interaction is modeled as a coupling between pressure and displacement the coupled problem is discretized in space domain with spectral elements and in time domain with central finite differences after discretization exact controllability problem is reformulated as a least squares problem which is solved by the conjugate gradient method

a level set based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two phase material model abstract this papers proposes a level set based topology optimization method for the simultaneous design of acoustic and structural material distributions in this study we develop a two phase material model that is a mixture of an elastic material and acoustic medium to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter in the proposed model boundary conditions at the two phase material boundaries are satisfied naturally avoiding the need to express these boundaries explicitly we formulate a topology optimization problem to minimize the sound pressure level using this two phase material model and a level set based method that obtains topologies free from grayscales the topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction diffusion equation several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure

numerical study and comparison of alternative time discretization schemes for an ultrasonic guided wave propagation problem coupled with fluid structure interaction abstract discretization is a crucial step in the numerical treatment of coupled multiphysics problems in the present paper we focus on the numerical solution of ultrasonic guided waves ugws propagation problem coupled with fluid structure interaction we track ugws propagation through fluid solid and their interface where the structure is in motion discretization is done via a finite element method for this we follow the rothe method in which discretization in time is followed by space discretization solving the resulting problem according to the monolithic approach further we provide a systematic analysis of alternative discretization schemes time steps and mesh refinements specifically we contrast one first order time discretization scheme cf backward euler and three second order schemes cf crank nicolson shifted crank nicolson and fractional step first we establish the robustness of the convergence result second we estimate the experimental order of convergence for alternative schemes and space time discretization combinations

kinetic growth walks and trails on oriented square lattices hull percolation and percolation hulls the authors have studied kinetic growth walks on the manhattan lattice and kinetic growth trails on the l lattice they find that the directional properties of these lattices prevent the kinetic growth walks from being trapped except at the origin as a consequence kgws are found to be in the skw universality class for these lattices extensive numerical calculations support this fact moreover it has been shown that the recently introduced hull percolation is equivalent to the kinetic growth walks on the manhattan lattice and the bond percolation hull on the square lattice at the percolation threshold is equivalent to the kinetic growth trails on the l lattice their numerical estimates agree nicely with the original estimates and thus support the equivalence

finite element computation of the vibration modes of a fluid solid system abstract in this paper we solve the interior elastoacoustic problem by a finite element method which does not present spurious or circulation modes for nonzero frequencies it consists of classical triangular lagrangian elements for the solid and lowest order triangular raviart thomas elements for the fluid transmission conditions at the fluid solid interface are taken into account in a weak sense numerical results for some test examples are presented which show the good performance of the proposed methodology

on a parabolic quadrilateral finite element for compressible flows abstract we present a 9 node finite element for compressible flow solutions a high order derivative upwind term and a shock capturing term are employed for stability and accuracy of the formulation we give the solutions of various example problems to illustrate our experiences with the element

an optimization based approach for solving a time harmonic multiphysical wave problem with higher order schemes this study considers developing numerical solution techniques for the computer simulations of time harmonic fluid structure interaction between acoustic and elastic waves the focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements we concentrate on the model in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement traditionally the complex valued time harmonic equations are used for solving the time harmonic problems instead of that we focus on finding periodic solutions without solving the time harmonic problems directly the time dependent equations can be simulated with respect to time until a time harmonic solution is reached but the approach suffers from poor convergence to overcome this challenge we follow the approach first suggested and developed for the acoustic wave equations by bristeau glowinski and periaux thus we accelerate the convergence rate by employing a controllability method the problem is formulated as a least squares optimization problem which is solved with the conjugate gradient cg algorithm computation of the gradient of the functional is done directly for the discretized problem a graph based multigrid method is used for preconditioning the cg algorithm

three dimensional viscous finite element formulation for acoustic fluid structure interaction abstract a three dimensional viscous finite element model is presented in this paper for the analysis of the acoustic fluid structure interaction systems including but not limited to the cochlear based transducers the model consists of a three dimensional viscous acoustic fluid medium interacting with a two dimensional flat structure domain the fluid field is governed by the linearized navier stokes equation with the fluid displacements and the pressure chosen as independent variables the mixed displacement pressure based formulation is used in the fluid field in order to alleviate the locking in the nearly incompressible fluid the structure is modeled as a mindlin plate with or without residual stress the hinton huang s 9 noded lagrangian plate element is chosen in order to be compatible with 27 4 u p fluid elements the results from the full 3d fem model are in good agreement with experimental results and other fem results including beltman s thin film viscoacoustic element w m beltman p j m van der hoogt r m e j spiering h tijdeman implementation and experimental validation of a new viscothermal acoustic finite element for acousto elastic problems j sound vib 216 1 1998 159 185 and two and half dimensional inviscid elements a a parthasarathi k grosh a l nuttall three dimensional numerical modeling for global cochlear dynamics j acoust soc am 107 2000 474 485 although it is computationally expensive it provides a benchmark solution for other numerical models or approximations to compare to besides experiments and it is capable of modeling any irregular geometries and material properties while other numerical models may not be applicable

symmetrization procedure for structure fluid cavity system involving pseudostatic correction this paper deals with a pressure displacement formulation based on the finite element method of an elastoacoustic coupling problem since directly solving the resulting system iscpu intensive for large models the solution is usually based on only a few uncoupled structural modes in vacuum and rigid cavity modes however this classical pressuredisplacement formulation leads to nonsymmetric eigenvalue problems furthermore if this method is accurate for weak coupling models significant errors occur when the truncated modes are coupled to the ones used in the analysis the present paper suggests a method combining the pseudostatic correction of the truncated modes in modal analysis with a symmetrization technique of the eigenvalue problems it allows the calculation of the real coupled modes and frequencies as well as the computation of an accurate elastoacoustic response even for the strong coupling of a structure with a heavy fluid liquid it is less cpu expensive than the classical method because it leads to a diagonalized system