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

separation of variables and exact solution to the dirac equation in curvilinear orthogonal coordinates with cylindrical symmetry in the present article a complete separation of variables in the dirac equation for a free particle is achieved in parabolic cylinder and elliptical coordinates the resulting system of ordinary differential equations is solved and the asymptotic behavior of the spinor solution is discussed

a dimension wise analysis method for the structural acoustic system with interval parameters abstract the interval structural acoustic analysis is mainly accomplished by interval and subinterval perturbation methods potential limitations for these intrusive methods include overestimation or interval translation effect for the former and prohibitive computational cost for the latter in this paper a dimension wise analysis method is thus proposed to overcome these potential limitations in this method a sectional curve of the system response surface along each input dimensionality is firstly extracted the minimal and maximal points of which are identified based on its legendre polynomial approximation and two input vectors i e the minimal and maximal input vectors are dimension wisely assembled by the minimal and maximal points of all sectional curves finally the lower and upper bounds of system response are computed by deterministic finite element analysis at the two input vectors two numerical examples are studied to demonstrate the effectiveness of the proposed method and show that compared to the interval and subinterval perturbation method a better accuracy is achieved without much compromise on efficiency by the proposed method especially for nonlinear problems with large interval parameters

existence of solutions for dirichlet problems with p laplacian an existence theorem of the solutions is obtained for the p laplacian equation with dirichlet boundary conditions by using the critical point theorem developed in song and tang 2006 10 martinez and rossi 2003 11 where f x t 0tf x s ds is assumed to lie between the two continuous eigenvalues k k 1 k 1 of the p laplacian

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

dirac equation in external vector fields separation of variables the method of separation of variables in the dirac equation in the external vector fields is developed through the search for exact solutions the essence of the method consists of the separation of the first order matricial differential operators that define the dependence of the dirac bispinor on the related variables but commutation of such operators with the operator of the equations or between them is not assumed this approach which is perfectly justified in the presence of gravitational fields permits one to prove rigorous theorems about necessary and sufficient conditions on the field functions that allow one to separate variables in the dirac equation in analogous investigations by other authors bagrov et al exact solutions of relativistic wave equations nauka novosibirst 1982 for electromagnetic fields an essential demand related to the operators that define the dependence of the bispinor on the separated variables is the demand for the commutation of a complete set of operators betw

existence and non existence results for a quasilinear problem with nonlinear boundary condition abstract we study the problem div a x u p 2 u 1 x 1 u q 2 u h x u r 2 u in r n a x u p 2 u n b x u p 2 u g x u on u 0 in where is an unbounded domain with smooth boundary n denotes the unit outward normal vector on and 0 are real parameters we assume throughout that p q r p pn n p 1 p n n 1 q n p p n while a b and h are positive functions we show that there exist an open interval i and 0 such that the problem has no solution if i and 0 furthermore there exist an open interval j i and 0 0 such that for any j the above problem has at least a solution if 0 but it has no solution provided that 0 0 our paper extends previous results obtained by j chabrowski and k pfluger

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

treatment of acoustic fluid structure interaction by localized lagrange multipliers formulation a new concept is presented for modeling the dynamic interaction between an acoustic fluid and an elastic structure the coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure and using node collocated lagrange multipliers to connect the frame to each subsystem the time domain response analysis is performed by a partitioned analysis procedure the main advantages of this localized lagrange multiplier llm primal dual coupling method are complete localization of the structure and fluid subsystems elimination of the conventional predictor in the partitioned time integration method and the ability to accommodate non matching meshes the standard newmark time integrator is used on both the fluid and structure models it is shown that if the integrator is a stable and second order accurate for a monolithic treatment it retains those properties for both mortar and llm partitioned solution procedures infinite and finite piston problems are used to explain and verify the methodology a sequel paper under preparation presents and discusses a set of benchmark and application examples that involve the response of existing dams to seismic excitation

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

resonance problems for the p laplacian systems abstract two existence theorems of the solutions are obtained for the p laplacian systems at resonance under a landesman lazer type condition by critical point theory

some existence theorems for elliptic resonant problems some existence theorems are obtained for the elliptic resonant problems at either the first eigenvalue or the higher eigenvalues with unbounded nonlinearity by using the minimax methods in critical point theory

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

finite element solution of incompressible fluid structure vibration problems in this paper we solve an eigenvalue problem arising from the computation of the vibrations of a coupled system incompressible fluid elastic structure in absence of external forces we use displacement variables for both the solid and the fluid but the fluid displacements are written as curls of a stream function classical linear triangular finite elements are used for the solid displacements and for the stream function in the fluid the kinematic transmission conditions at the fluid solid interface are taken into account in a weak sense by means of a lagrange multiplier the method does not present spurious or circulation modes for non zero frequencies numerical results are given for some test cases 1997 by john wiley sons ltd

separation of variables and exact solution of the dirac equation in nonstatic minkowski spacetimes using a second order formalism a complete separation of variables in the dirac equation for a free particle in nonstatic orthogonal curvilinear coordinates of the form t f u v x g u v y z is presented it is shown that the dirac equation is separable in eight nonequivalent coordinate systems where the klein gordon equation separates exact solutions of the dirac equation in the systems of coordinates obtained are presented

partitioned formulation of internal fluid structure interaction problems by localized lagrange multipliers abstract a partitioned formulation of compressible internal fluid structure interaction problems is presented by employing a displacement model for both the fluid and structure partitioning is effected by a localized version of the method of lagrange multipliers which assigns two independent sets of lagrange multipliers to the structural and fluid interfaces two major features of the present formulation include an interface compliance normalization that helps capture the predominant physics of interaction phenomena when the interfaces are characterized by two radically different rigidities and a novel transformation of the displacement model into a fluid pressure model that is suitable for both transient and vibration analyses the present formulation first solves for the interface lagrange multipliers which are subsequently used to solve for the structural displacements and the fluid displacement or pressure by employing two independent analysis modules

resonance problems for p q laplacian systems abstract some existence results of weak solutions are established for p q laplacian systems which are resonant at an arbitrary eigenvalue by the minimax methods in critical point theory

resonance problems for the p laplacian with a nonlinear boundary condition abstract consider resonance problems at an arbitrary eigenvalue of the elliptic equations p u u p 2 u g 1 u h 1 x in u p 2 u u p 2 u g 2 u h 2 x on some existence theorems are obtained under the landesman lazer type conditions by using variational method

positive solutions of elliptic equations with nonlinear boundary conditions abstract this paper deals with the nonlinear elliptic equation u u f x u in a bounded smooth domain r n with a nonlinear boundary value condition the existence results are obtained by the sub supersolution method and the mountain pass lemma and nonexistence is also considered

remarks on multiple nontrivial solutions for quasi linear resonant problems in this paper morse theory and local linking are used to study the existence of multiple nontrivial solutions for a class of dirichlet boundary value problems with double resonance at infinity and at 0

a reduction method for structure acoustic and poroelastic acoustic problems using interface dependent lanczos vectors a reduction method is proposed for analysing structure acoustic and poroelastic acoustic problems within a finite element framework this includes systems consisting of an acoustic fluid domain coupled to a flexible structural domain and or a porous sound absorbing material domain the studied problem is reduced by dividing the system into a number of physical subdomains a set of basis vectors is derived for each of these subdomains including both normal modes and interface dependent vectors that take account of the influence of connecting subdomains the method is verified in two numerical examples using the proposed method for both solving the structure acoustic eigenvalue problem and performing a frequency response analysis in an acoustic cavity with one wall covered by porous material c 2005 elsevier b v all rights reserved less

solvability for two point boundary value problems abstract suppose that h l 1 0 g c r r and lim t g t t 0 with the saddle point theorem the solvability is proved for the two point boundary value problemproblem formula under the condition that formula where formula and formula

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

on separable pauli equations we classify 1 3 dimensional pauli equations for a spin 12 particle interacting with the electro magnetic field that are solvable by the method of separation of variables as a result we obtain the 11 classes of vector potentials of the electro magnetic field a t x a0 t x a t x providing separability of the corresponding pauli equations it is established in particular that the necessary condition for the pauli equation to be separable into second order matrix ordinary differential equations is its equivalence to the system of two uncoupled schrodinger equations in addition the magnetic field has to be independent of spatial variables we prove that coordinate systems and the vector potentials of the electro magnetic field providing the separability of the corresponding pauli equations coincide with those for the schrodinger equations furthermore an efficient algorithm for constructing all coordinate systems providing the separability of pauli equation with a fixed vector potential of t

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

partitioned formulation of internal and gravity waves interacting with flexible structures abstract this paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures the governing interaction model consists of three completely partitioned entities fluid model structural model and interface model that acts as an internal constraint on the fluid structure interface boundary thus the proposed partitioned multi physics modeling can employ two completely modular fluid and structure software modules plus an interface solver hence amenable to partitioned solution algorithms the interface discretization can exploit the nonmatching interface algorithm previously developed via the method of localized lagrange multipliers also noted is that the present fluid model can make use of widely available finite element software for standard poisson type problems

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

solvability of the forced duffing equation at resonance some existence theorems are obtained for periodic solutions of the forced duffing equation at resonance by the minimax methods

resonance problems for the p laplacian abstract we consider resonance problems at an arbitrary eigenvalue of the p laplacian and prove the existence of weak solutions assuming a standard landesman lazer condition we use variational arguments to characterize certain eigenvalues and then to establish the solvability of the given boundary value problem

the classification of complete sets of operators commuting with the dirac operator in minkowski space time under the action of the poincare group p 1 3 the three four and five dimensional vector spaces of formally self adjoint first order matrix differential operators commuting among themselves and with the dirac operator are classified this gives a complete classification of the maximal subspaces of the vector space of first order formally self adjoint matrix differential operators commuting with the dirac operator which form an abelian lie algebra under the commutator

existence results for the p laplacian with nonlinear boundary conditions in this paper we study the existence of nontrivial solutions for the problem pu u p 2u in a bounded smooth domain rn with a nonlinear boundary condition given by u p 2 u f u on the boundary of the domain the proofs are based on variational and topological arguments

on separable solutions of dirac s equation for the electron the properties of coordinate systems that admit separation of the laplacian and hamilton jacobi operators have been thoroughly explored so that the nature of solutions in separable form of laplace s equation the wave equation schrodinger s equation and the hamilton jacobi equation are well understood the corresponding problems for the dirac operator in flat space time have been less completely examined and this paper contains studies intended to produce a more systematic account of possible solutions of dirac s equation because the dirac operator differs from the laplacian in being a first degree differential operator and in having matrix coefficients it is not possible to discuss possible solutions in as general a way and the separable solutions are far less rich than for equations with the laplacian in particular the forms of the potentials for which separable solutions are possible are not for the most part of physical interest although the discussion is confined to coordinates in flat space time some of the procedures are derived from those developed to solve dirac s equation in coordinates with a kerr metric

a local mountain pass theorem and applications to a double perturbed p x laplacian equations in this paper we prove a local mountain pass theorem without p s condition using this theorem and ricceri s variational principle we consider a double perturbed neumann problem with nonlinear boundary condition of the email protected p x u a x u p x 2u f x u email protected 1 x u email protected u p x email protected email protected email protected g x u email protected 2 x u email protected email protected least seven solutions are obtained under different assumptions

strong resonance for some quasilinear elliptic equations abstract we study the existence of the weak solutions of the nonlinear boundary value problem p u 1 u p 2 u g u h x in u 0 on where the nonlinearity g is of the landesman lazer type our sufficient conditions generalize all previously published results about the strong resonance at the first eigenvalue

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

nonexistence existence and multiplicity of positive solutions to the p x laplacian nonlinear neumann boundary value problem abstract we study the nonexistence existence and multiplicity of positive solutions for the nonlinear neumann boundary value problem involving the p x laplacian of the form p x u u p x 2 u f x u in u p x 2 u g x u on where is a bounded smooth domain in r n p c 1 and p x 1 for x using the sub supersolution method and the variational principles under appropriate assumptions on f and g we prove that there exists 0 such that the problem has at least two positive solutions if has at least one positive solution if and has no positive solution if