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

fuzzy t net theory abstract in this paper we define the convergence of fuzzy nets in a fuzzy topological space x by means of the family of its level topologies l t t 0 1 introduced in 4 by lowen fuzzy t nets and fuzzy t ultranets are also characterized and relations between t prefilters and fuzzy t nets are studied getting analogous results to those of general topology

t prefilter theory abstract in the first part of this paper the notion of t prefilter is introduced and studied as are the applications t and t their properties and relations between them we characterize the minimal prime t prefilters finer than a given t prefilter by using ultrafilters on x and we give equivalents conditions of the t maximality in the second part we define t convergence and we obtain a characterization of t compactness gantner steinlage by means of the maximal t prefilters finally some applications of these concepts related to the continuity separation axioms and fuzzy compactness are studied

image decomposition method for the analysis of a mixed dislocation in a general multilayer the elastic solutions for a mixed dislocation in a general multilayer with n dissimilar anisotropic layers are obtained via a generalized image decomposition method the original problem is decomposed into n homogeneous subproblems with strategically placed continuously distributed image virtual dislocations which satisfy the consistency conditions for degen erate nm m n layer problems the image dislocations are used to satisfy the interface or free surface conditions and represent the unknowns of the problem the resulting singular cauchy integral equations are transformed into non singular fredholm integral equations of the second kind using certain h and i integral transforms the fredholm integral equations are then solved via the classical nystrom method the general decomposition and the elimination of all singular integrals yield an exact formulation of the problem the approximation arises only in the nystrom method the dislocation mixity and the number of layers dissimilar in thickness and elastic anisotropy can be handled without difficulty constrained only by the number of linear algebraic equations in the nystrom method for large n for the numerical study image forces on a dislocation in two and three layer systems are calculated the accuracy of the results is verified by checking the boundary conditions and by comparison with previous results the dependence of the image force on the dislocation position and mix ity and on the layer thicknesses and elastic anisotropies is also illustrated via numerical investigations 2006 elsevier ltd all rights reserved

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

finite element approximation of a displacement formulation for time domain elastoacoustic vibrations this paper deals with the numerical solution of a system of second order in time partial differential equations modeling the vibrations of a coupling between an elastic solid and an inviscid compressible fluid both media are described in terms of their respective displacement fields the problem is solved in the time domain by combining a newmark s scheme for time discretization with a finite element method for space discretization the latter combines standard lagrangian elements in the solid with lowest order raviart thomas elements in the fluid stability is proved and numerical results showing the good behavior of the method are reported

full field analysis of a planar anisotropic layered half plane for concentrated forces and edge dislocations the problem of a planar anisotropic elastic layered halfplane subjected to concentrated forces and edge dislocations applied either in the layer or in the halfplane is analysed one of the objectiv

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

spectral approximation of quadratic operator polynomials arising in photonic band structure calculations galerkin spectral approximation theory for non self adjoint quadratic operator polynomials with periodic coefficients is considered the main applications are complex band structure calculations in metallic photonic crystals periodic waveguides and metamaterials we show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part the spectral problem is equivalent to a non compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator convergence rates of finite element discretizations are considered and numerical experiments with the p p version and the h h version of the finite element method confirm the theoretical convergence rates

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

finite element vibration analysis of fluid solid systems without spurious modes this paper deals with the finite element approximation of the vibration modes of a problem with fluid structure interaction displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation we introduce a nonconforming discretization error estimates for the approximation of eigenvalues and eigenvectors are given

a pade approximate linearization algorithm for solving the quadratic eigenvalue problem with low rank damping a pad e approximate linearization algorithm for solving the quadratic eigenvalue problem with low rank damping ding lu xin huang zhaojun bai yangfeng su june 30 2014 abstract the low rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations to exploit the low rank damping property we propose a pad e approximate linearization pal algorithm the advantage of the pal algorithm is that the dimension of the resulting linear eigenvalue problem is only n lm which is generally substantially smaller than the dimension 2n of the linear eigenvalue problem produced by a direct linearization approach where n is the dimension of the quadratic eigenvalue problem l and m are the rank of the damping matrix and the order of a pad e approximant respectively numerical examples show that by exploiting the low rank damping property the pal algorithm runs 33 47 faster than the direct linearization approach for solving modest size quadratic eigenvalue problems introduction we consider the quadratic eigenvalue problem qep q x 2 m c k x 0 where m c and k are n n matrices referred to as mass damping and stiffness matrices respectively in structural dynamics analysis the low rank damping property refers to the case where the damping matrix c is of rank l l n and admits the rank revealing decomposition c ef t where e and f are n l full column rank matrices the qep with the low rank damping arises frequently from analysis of structural dynam ics 10 18 and structural acoustic interaction 3 6 32 in these applications the damping school of mathematical sciences fudan university shanghai 200433 p r china dinglu fudan edu cn part of this work was done while this author was visiting at university of california davis supported by china scholarship council school of mathematical sciences fudan university shanghai 200433 china xinhuang fudan edu cn part of this work was done while this author was visiting at university of california davis supported by china scholarship council department of computer science and department of mathematics university of california davis ca 95616 usa bai cs ucdavis edu school of mathematical sciences fudan university shanghai 200433 china yfsu fudan edu cn

approximation of eigenvalues in mixed form discrete compactness property and application to hp mixed finite elements abstract in this paper we discuss the discrete compactness property dcp which is a well known tool for the analysis of finite element approximations of maxwell s eigenvalues we restrict our presentation to maxwell s eigenvalues but the theory applies to more general situations and in particular to mixed finite element schemes that can be written in the framework of de rham complex and which enjoy suitable compactness properties we investigate the relationships between dcp and standard mixed conditions for the good approximation of eigenvalues as a consequence of our theory the convergence analysis of the rectangular hp version of raviart thomas finite elements for the approximation of laplace eigenvalues is presented as a corollary of the analogous result for hp edge elements applied to the approximation of maxwell s eigenvalues d boffi m costabel m dauge l demkowicz discrete compactness for the hp version of rectangular edge finite elements siam j numer anal 44 3 2006 979 1004

a high order discontinuous galerkin approach to the elasto acoustic problem abstract we address the spatial discretization of an evolution problem arising from the coupling of elastic and acoustic wave propagation phenomena by employing a discontinuous galerkin scheme on polygonal and polyhedral meshes the coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid elastic and fluid acoustic domains we state and prove a well posedness result for the strong formulation of the problem present a stability analysis for the semi discrete formulation and finally prove an a priori h p version error estimate for the resulting formulation in a suitable mesh dependent energy norm we also discuss the time integration scheme employed to obtain the fully discrete system the convergence results are validated by numerical experiments carried out in a two dimensional setting

a posteriori error estimates in finite element acoustic analysis we present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies we prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement

a parametric study on fluid structure interaction problems abstract this paper deals with finite element analysis of the fluid structure systems considering the coupled effect of elastic structure and fluid the equations of motion of the fluid considered inviscid and compressible are expressed in terms of the pressure variable alone the elastic structure and the fluid domain are treated as two separate systems and discretized with finite elements the solution of the coupled system is accomplished by solving the two systems separately with the interaction effects at the fluid solid interface enforced by a developed iterative scheme non divergent pressure and displacement are obtained simultaneously through a few numbers of iterations studies show the accuracy of the proposed algorithm while comparing with the existing ones available in the literature the parametric study of the coupled system shows the importance of fluid height and material property of the structure

efficient and reliable hp fem estimates for quadratic eigenvalue problems and photonic crystal applications we present a posteriori analysis of higher order finite element approximations hp fem for quadratic fredholm valued operator functions residual estimates for approximations of the algebraic eigenspaces are derived and we reduce the analysis of the estimator to the analysis of an associated boundary value problem for the reasons of robustness we also consider approximations of the associated invariant pairs we show that our estimator inherits the efficiency and reliability properties of the underlying boundary value estimator as a model problem we consider spectral problems arising in analysis of photonic crystals in particular we present an example where a targeted family of eigenvalues cannot be guaranteed to be semisimple numerical experiments with hp fem show the predicted convergence rates the measured effectivities of the estimator compare favorably with the performance of the same estimator on the associated boundary value problem we also present a benchmark estimator based on the dual weighted residual dwr approach which is more expensive to compute but whose measured effectivities are close to one

spectral approximation for polynomial eigenvalue problems abstract in this paper we extent the classical spectral approximation theory for compact and bounded operators to general linear operators and then apply it to polynomial eigenvalue problems pep we also study the essential spectrum in peps and prove that this spectrum is stable under relatively compact perturbations based on this analysis we give some suggestions to make algorithms for solving peps more efficient

finite element analysis of the vibration problem of a plate coupled with a fluid we consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid the plate is modelled by reissner mindlin equations while the fluid is described in terms of displacement variables this formulation leads to a symmetric eigenvalue problem reissner mindlin equations are discretized by a mixed method the equations for the fluid with raviart thomas elements and a non conforming coupling is used on the interface in order to prove that the method is locking free we consider a family of problems one for each thickness t 0 and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t to 0 we prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t finally we present numerical results confirming the good performance of the method

accurate pressure post process of a finite element method for elastoacoustics this paper deals with a post process to obtain a more accurate approximation of the fluid pressure from a finite element computation of the vibration modes of a fluid structure coupled system the underlying finite element method based on a displacement formulation for both media consists of using raviart thomas elements for the fluid combined with standard continuous elements for the solid an easy to compute post process of the pressure is derived the relation between this post process and an alternative finite element approximation of the problem based on discretizing the fluid pressure by enriched crouzeix raviart elements is studied higher order estimates for the l2 norm of the post processed pressure are proved by exploiting this relation as a by product higher order l2 estimates for the solid displacements obtained with the original method are also proved

the elastic fields of a dislocation in ananisotropic strip abstract the elastic fields of a dislocation in a general anisotropic strip are analysed the analysis is made by using the stroh formalism for anisotropic elasticity in conjunction with the fourier transform the surfaces of the strip are considered either free or fixed the image forces on an edge dislocation in tungsten and potassium are computed as functions of the position of the dislocation and the inclination of the slip planes the interactive forces between two like dislocations on the same slip plane are also calculated

mixed finite element methods in fluid structure systems the eigenvalue problem describing the frequencies of a fluid vibrating in a rigid cavity or within moving boundaries is considered based on the method of lagrange multipliers a three field mixed formulation is introduced in order to avoid the spurious circulating modes stability and optimal error bounds are proved for two choices of finite element spaces

on fuzzy subnets abstract in general topology there is a close paralellism between the theories of convergence of nets and of filters in which subnet corresponds to finer filter but this relationship depends on the notion of subnet that one uses various authors have defined for fuzzy topological spaces the convergence of fuzzy filters and fuzzy nets and have obtained connections between these theories however these authors do not obtain a satisfactory relation between a fuzzy net and the fuzzy net based on the prefilter generated by it in this paper we define for fuzzy nets a new notion of fuzzy subnet that solves this question

a new finite element formulation for internal acoustic problems with dissipative walls this work concerns the variational formulation and the numerical computation of internal acoustic problems with absorbing walls the originality of the proposed approach compared to other existing methods is the introduction of the normal fluid displacement field on the damped walls this additional variable allows to transpose formulations in frequency domain to time domain when the fluid is described by a scalar field pressure or fluid displacement potential with this new scalar unknown various absorbing wall models can be introduced in the variational formulation moreover the associated finite element matrix system in symmetric form can be solved in frequency and time domain

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

a virtual element method for the acoustic vibration problem we analyze in this paper a virtual element approximation for the acoustic vibration problem we consider a variational formulation relying only on the fluid displacement and propose a discretization by means of mathrm h mathrm div h div virtual elements with vanishing rotor under standard assumptions on the meshes we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates with this end we prove approximation properties of the proposed virtual elements we also report some numerical tests supporting our theoretical results

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

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 analysis of pressure formulation of the elastoacoustic problem in this paper we analyze the non symmetric pressure displacement formulation of the elastoacoustic vibration problem and show its equivalence with the symmetric stiffness coupling formulation we introduce discretizations for these problems based on lagrangian finite elements we show that both formulations are also equivalent at discrete level and prove optimal error estimates for eigenfunctions and eigenvalues both formulations are rewritten such as to be solved with a standard matlab eigensolver we report numerical results comparing the efficiency of the methods over some test examples

the order of convergence of eigenfrequencies in finite element approximations of fluid structure interaction problems in this paper we prove a double order for the convergence of eigenfrequencies in fluid structure vibration problems we improve estimates given recently for compressible and incompressible fluids to do this we extend classical results on finite element spectral approximation to nonconforming methods for noncompact operators

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

finite element computation of three dimensional elastoacoustic vibrations abstract in this paper the interior elastoacoustic problem in a 3d domain is solved displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation a non standard discretization is used consisting of classical linear tetrahedral finite element for the solid and raviart thomas elements of lowest order for the fluid a new unknown is introduced on the interface between solid and fluid to impose the transmission conditions

elastic study on singularities interacting with interfaces using alternating technique part i anisotropic trimaterial abstract schwarz neumann s alternating technique is applied to singularity problems in an anisotropic trimaterial which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces linear elastic materials under general plane deformations are assumed in which the plane of deformation is perpendicular to the two parallel interface planes it is well known that if the solution is known for singularities in a homogeneous anisotropic medium the solution for the same singularities in an anisotropic bimaterial can be constructed by the method of analytic continuation it is shown here that the solution for singularities in a homogeneous medium may also be used as a base of the solution for the same singularities in a trimaterial the alternating technique is applied to derive the trimaterial solution in a series form whose convergence is guaranteed the solution procedure is universal in the sense that no specific information about the singularity is needed the energetic forces exerted on a dislocation due to interfaces are also evaluated from the trimaterial solution the trimaterial solution studied here can be applied to a variety of problems e g a bimaterial including a half plane problem a finite thin film on semi infinite substrate and a finite strip of thin film etc some examples are presented to verify the usefulness of the obtained solutions

a highly accurate discontinuous galerkin method for complex interfaces between solids and moving fluids we have extended a new highly accurate numerical scheme for unstructured 2d and 3d meshes based on the discontinuous galerkin approach to simulate seismic wave propagation in heterogeneous media containing fluid solid interfaces because of the formulation of the wave equations as a unified first order hyperbolic system in velocity stress the fluid can be in movement along the interface the governing equations within the moving fluid are derived from well known first principles in fluid mechanics the discontinuous galerkin approach allows for jumps of the material parameters and the solution across element interfaces which are handled by riemann solvers or numerical fluxes the use of riemann solvers at the element interfaces makesthe treatment of the fluid particularly simple bysetting the shearmodulus in the fluid region to zero no additional compatibility relations such as vanishing shear stress or continuity of normal stresses are necessary to couple the solid and fluid along an interface the

analysis of a finite element method for pressure potential formulation of elastoacoustic spectral problems a finite element method to approximate the vibration modes of a structure enclosing an acoustic fluid is analyzed the fluid is described by using simultaneously pressure and displacement potential variables whereas displacement variables are used for the solid a mathematical analysis of the continuous spectral problem is given the problem is discretized on a simplicial mesh by using piecewise constant elements for the pressure and continuous piecewise linear finite elements for the other fields error estimates are settled for approximate eigenvalues and eigenfrequencies finally implementation issues are discussed

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 n convergence of fuzzy nets abstract in this paper we define the n convergence of fuzzy nets in a fuzzy topological space and we use it to give a characterization of some fuzzy topological concepts we give necessary conditions for the n convergence of fuzzy nets in a fuzzy topological space and we characterize this n convergence in a topologically generated fuzzy topological space we also study some characterizations of fuzzy ultranets and we introduce the concept of subordination between fuzzy nets we associate to each fuzzy net in x a prefilter on x and conversely and we give an exhaustive description of the connections between these two theories we give a theory of fuzzy convergence classes and we characterize fuzzy topologies via some special types of fuzzy convergence classes

finite element analysis for a pressure stress formulation of a fluid structure interaction spectral problem the aim of this paper is to analyze an elastoacoustic vibration problem employing a dual mixed formulation in the solid domain the cauchy stress tensor and the rotation are the primary variables in the elastic structure while the standard pressure formulation is considered in the acoustic fluid the resulting mixed eigenvalue problem is approximated by a conforming galerkin scheme based on the lowest order lagrange and arnold falk winther finite element subspaces in the fluid and solid domains respectively we show that the scheme provides a correct approximation of the spectrum and prove quasi optimal error estimates finally we report some numerical experiments

on the spurious solutions in the high order finite difference methods for eigenvalue problems in this paper the origins of spurious solutions occurring in the high order finite difference methods are studied based on a uniform mesh spurious modes are found in the high order one sided finite difference discretizations of many eigenvalue problems spurious modes are classified as spectral pollution and non spectral pollution the latter can be partially avoided by mesh refinement while the former persists when the mesh is refined through numerical studies of some prototype eigenvalue problems such as those of the helmholtz and beam equations we show that perfect central differentiation schemes do not produce any spurious modes nevertheless high order central difference schemes encounter difficulties in implementing complex boundary conditions we further show that the central difference schemes will produce spurious modes as well if asymmetric approximation is involved in boundary treatments in general central difference schemes are less likely to produce spurious modes than one sided difference schemes 2007 elsevier b v all rights reserved