on differential games for infinite dimensional systems with nonlinear unbounded operators abstract we consider a two player zero sum differential game governed by an abstract nonlinear differential equation of accretive type in an infinite dimensional space we prove that the value function of the game is the unique viscosity solution of the corresponding hamilton jacobi isaacs equation in the sense of 12 we also discuss some properties of this notion of solution

green s matrix and the boundary integral equation method for the analysis of vibration and energy flow in cylindrical shells with and without internal fluid loading abstract this paper presents several aspects of the dynamics of a cylindrical shell with and without heavy internal fluid loading which have not been studied before in detail firstly a consistent formulation of boundary integral equations for a shell of finite length is derived based on the energy conservation principle and the reciprocity theorem this derivation naturally leads to identification of principal components of the energy flux through an arbitrary cross section of a shell and to formulation of green s matrix for an infinitely long shell at each individual circumferential wave number secondly an inspection into the energy re distribution between several transmission paths in a near field in a boundary layer at the vicinity of a loaded cross section is performed which sheds light on the role of evanescent waves in motions of a driven shell thirdly the influence of excitation conditions on steady fluctuations of the overall energy flow between transmission paths in a far field is explored for the case when several propagating waves exist in a shell both with and without internal fluid loading besides a systematic verification of the solution offered by the boundary equations method is given through comparison of eigenfrequencies with those computed in finite element modelling for various boundary conditions analysis of dispersion curves and input mobilities is also presented

a zero sum differential game in a hilbert space we study a zero sum differential game of fixed duration in a separable hilbert space we prove a minimax principle and establish the equivalence between the dynamic programming principle and the existence of a saddle point equilibrium we also prove sufficient conditions for optimality

recursive based pcg methods for toeplitz systems with nonnegative generating functions in this paper we consider the solutions of symmetric positive definite but ill conditioned toeplitz systems an x b here we propose to solve the system by the recursive based preconditioned conjugate gradient method the idea is to use the inverse of am the principal submatrix of an with the gohberg semencul formula as a preconditioner for an the inverse of am can be generated recursively by using the formula until m is small enough the construction of the preconditioners requires only the entries of an and does not require the explicit knowledge of the generating function f of an we show that if f is a nonnegative bounded and piecewise continuous even function with a finite number of zeros of even order the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers hence the conjugate gradient method when applied to solving the preconditioned system converges very quickly numerical results are included to illustrate the effectiveness of our approach

block triangular preconditioners based on symmetric triangular decomposition for generalized saddle point problems abstract in this paper the symmetric triangular decomposition is further studied to construct a class of block triangular preconditioners for generalized saddle point problems such that the preconditioned generalized saddle point matrices are symmetric and positive definite then the preconditioned conjugate gradient iterative method can be used three specific preconditioners are studied in detail eigen properties of the corresponding preconditioned generalized saddle point matrices are studied in particular upper bounds on the condition number of the preconditioned matrices are analyzed finally numerical experiments of a model stokes equation are given to illustrate the efficiency of the new proposed preconditioners

on inexact preconditioners for nonsymmetric matrices inexact versions of the block triangular preconditioners for nonsymmetric matrices of block two by two structures in m f murphy g h golub and a j wathen siam j sci comput 21 2000 pp 1969 1972 and i c f ipsen siam j sci comput 23 2001 pp 1050 1051 are presented and the two preconditioners for symmetric block two by two matrices in c durazzi and v ruggiero numer linear algebra appl 10 2003 pp 673 688 are extended to general nonsymmetric matrices moreover we precisely describe the spectral properties of the preconditioned matrices and the finite step termination properties of the preconditioned krylov subspace iteration methods with an optimal or galerkin property with respect to these preconditioners several numerical examples are performed to illustrate the effectiveness of the proposed preconditioners

eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems in this paper an indefinite block triangular preconditioner for symmetric saddle point problems is discussed the bounds for all the real eigenvalues of the preconditioned matrix are provided and the bounds for the real and imaginary parts of all the complex eigenvalues of the preconditioned matrix are also provided the corresponding theoretical results of paper by bergamaschi 2012 are improved numerical experiments are reported to confirm our theoretical results

on convergence and semi convergence of ssor like methods for augmented linear systems abstract in this paper we analyze the convergence and semi convergence of a class of ssor like methods with four real functions for augmented systems the class takes most existed ssor like methods as its special cases for nonsingular systems we obtain the minimum of convergence factors of all the ssor like methods in the class and study when it can be reached by the convergence factors of methods in the class by considering the equivalence of methods we show that most of the existed ssor like methods have the same minimum of convergence factors

a note on preconditioning for indefinite linear systems preconditioners are often conceived as approximate inverses for nonsingular indefinite matrices of saddle point or kkt form we show how preconditioners incorporating an exact schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues thus approximations of the schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses

a note on preconditioning nonsymmetric matrices the preconditioners for indefinite matrices of kkt form in m f murphy g h golub and a j wathen siam j sci comput 21 2000 pp 1969 1972 are extended to general nonsymmetric matrices

robust preconditioners for optimal control with time periodic parabolic equation abstract based on a new approximation of a schur complement matrix and some preconditioning techniques considered in earlier papers three robust preconditioners are presented for solving the kkt systems arising from discretizing optimal control problem with time periodic parabolic equation the eigenvalue bounds of the preconditioned matrices and some new theoretical results are obtained moreover selection of quasi optimal parameter is studied and an explicit expression of the quasi optimal parameter is given numerical examples are given to illustrate the effectiveness of the three proposed optimized preconditioners

a note on the positive stable block triangular preconditioner for generalized saddle point problems abstract in this paper we give a sharp eigenvalue bound for the positive stable block triangular preconditioned matrix presented in a recent paper by cao z h cao positive stable block triangular preconditioners for symmetric saddle point problems appl numer math 57 2007 899 910 the intervals containing these eigenvalues of the preconditioned matrix remove the origin which is benefit for further study numerical experiments of a model stokes problem are presented to show the estimate and the effectiveness of the positive stable block triangular preconditioners

a generalized relaxed positive definite and skew hermitian splitting preconditioner for non hermitian saddle point problems for non hermitian saddle point problems with the non hermitian positive definite 1 1 block zhang et al 2014 presented a relaxed positive definite and skew hermitian splitting rpss preconditioner to accelerate the convergence rates of the krylov subspace iteration methods such as gmres in this paper the convergence property of the grpss iteration method is proved and a generalized rpss grpss preconditioner is proposed the grpss preconditioner is much closer to the coefficient matrix than the rpss preconditioner in certain norm which straightforwardly results in an grpss iteration method we employing the grpss preconditioner to accelerate some krylov subspace methods like gmres the spectral distribution of the preconditioned matrix is described and an upper bound of the degree of the minimal polynomial of the preconditioned matrix is obtained finally numerical experiments of a model navier stokes equation are presented to illustrate the efficiency of the grpss preconditioner

preconditioning of complex linear systems from the helmholtz equation abstract in this paper for solving a class of complex linear systems from the helmholtz equation efficiently a new splitting preconditioner is established and a real valued preconditioned iterative method is presented spectral properties of the preconditioned matrix are discussed and bound on the eigenvalues of the preconditioned matrix is given theorem which provides the dimension of the krylov subspace methods for the preconditioned iteration method is obtained the implementation of the preconditioned method is given and the optimal choice of the accelerated parameter is derived in particular a more practical way to choose the accelerated parameter is also proposed numerical experiments arising from the helmholtz equation are used to illustrate the performance of the preconditioner which show the effectiveness and robustness of the new preconditioned gmres method and demonstrate meshsize independent and wave number insensitive convergence behavior

on advantages of derivation of exact dynamical stiffness matrices from boundary integral equations dynamical stiffness matrices are broadly used for solving problems in wave propagation in elastic structures for elastic waveguides that support both propagating and evanescent waves the standard use of transfer matrices to obtain their dynamical stiffness matrix may cause problems in computations in this letter to the editor an advanced way to derive dynamical stiffness matrices is proposed and exemplified in the classical bernoulli euler beam theory

on hybrid preconditioning methods for large sparse saddle point problems abstract based on the block triangular product approximation to a 2 by 2 block matrix a class of hybrid preconditioning methods is designed for accelerating the minres method for solving saddle point problems the appropriate values for the parameters involved in the new preconditioners are estimated so that the numerical conditioning and the spectral property of the saddle point matrix of the linear system can be substantially improved several practical hybrid preconditioners and the corresponding preconditioning iterative methods are constructed and studied too

hamilton jacobi equations in infinite dimensions iii on etudie des equations de la forme f x u du 0 dans ou est un sous ensemble ouvert d un espace de banach v la fonction inconnue u r est continue du x est la derivee de frechet de u en x et f est une fonction non lineaire qui est une application continue de r v dans r on introduit la notion de solution viscosite stricte afin d eliminer l hypothese que v a la propriete de radon nikodym

bi orthogonality relations for fluid filled elastic cylindrical shells theory generalisations and application to construct tailored green s matrices abstract the paper addresses the classical problem of time harmonic forced vibrations of a fluid filled cylindrical shell considered as a multi modal waveguide carrying infinitely many waves the forced vibration problem is solved using tailored green s matrices formulated in terms of eigenfunction expansions the formulation of green s matrix is based on special bi orthogonality relations between the eigenfunctions which are derived here for the fluid filled shell further the relations are generalised to any multi modal symmetric waveguide using the orthogonality relations the transcendental equation system is converted into algebraic modal equations that can be solved analytically upon formulation of green s matrices the solution space is studied in terms of completeness and convergence uniformity and rate special features and findings exposed only through this modal decomposition method are elaborated and the physical interpretation of the bi orthogonality relation is discussed in relation to the total energy flow which leads to derivation of simplified equations for the energy flow components

vibroacoustic response of a thin cylindrical shell excited by a turbulent internal flow comparison between numerical prediction and experimentation the main aspect of this work is to establish a comparison between the measured and the modelled vibroacoustic response of a thin cylindrical pipe excited by a turbulent internal flow the first part presents the experiment a corcos like model of the wall pressure fluctuation is proposed the vibroacoustic response of the shell is measured a numerical method based on a boundary integral formulation and a matched asymptotic expansion is developed computed spectral densities of the velocity of and acoustic sound pressure radiated by the shell are compared with experimental results the comparison shows an agreement within a few decibels

convergence properties of preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite matrices for the non hermitian and positive semidefinite systems of linear equations we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned hermitian and skew hermitian splitting iteration methods we then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned hermitian and skew hermitian splitting iteration methods

analysis of the energy transmission in compound cylindrical shells with and without internal heavy fluid loading by boundary integral equations and by floquet theory abstract this paper addresses three aspects of the steady state free vibration of non uniform i e composed of alternating elements elastic cylindrical shells with and without internal heavy fluid loading which have not previously been studied in detailed form firstly floquet theory is applied to detect the location of frequency band gaps in an infinitely long periodic fluid filled cylindrical shell vibrating in the beam type mode m 1 and in the ovalling mode m 2 in the framework of two simplified theories as a prerequisite for this study the validity range of these theories is estimated by comparison of the resulting dispersion curves with the exact solution secondly the boundary equations are derived for a cylindrical shell with internal heavy fluid loading in the framework of the suggested theories the methodology of boundary integral equations is used to obtain exact solutions for the problems of free vibrations of a finite shell and wave propagation in an infinitely long shell finally the energy transmission in a semi infinite non uniform cylindrical shell with and without internal heavy fluid loading is addressed predictions obtained by use of floquet theory are compared with the exact solution obtained by the method of boundary integral equations

vibrational energy flow in elastic circular cylindrical shells abstract the expressions are evaluated given in terms of the characteristic shell s components of motions axial tangential and radial for the axial and the circumferential component of the unit energy flow i e the energy flow per unit width along the shell s wall these expressions contain the same terms as the corresponding expressions for flat plates membrane and flexural plus an additional term dependent on curvature which results from the intercoupling between that three orthogonal components of motion on the basis of the modal representation of the shell s motion an analysis was made of the influence of the three different terms which contribute to the total energy flow depending on the frequency region considered the three terms exhibit considerable variations in contributing the total energy flow by averaging the energy flow in the circumferential and the axial directions simplifications of governing formulae are achieved in this way measurements can be accomplished without the need for excessive equipment and processing

splitting based block preconditioning methods for block two by two matrices of real square blocks recently bai proposed rotated block preconditioners for block two by two matrices of real square blocks these rotated block preconditioners have the product form of a scaled orthogonal matrix and a block two by two triangular matrix theoretical and numerical results have shown the superiority of these rotated block preconditioners see bai 2013 10 in this paper inspired by the efficiency and the special structure of the rotated block preconditioners we establish a new equivalent linear system to the original linear system in which an orthogonal matrix arises we construct block jacobi and block gauss seidel splitting iteration methods based on the coefficient matrix of the new linear system the convergence of these splitting iterations is also demonstrated then by utilizing the proposed block jacobi and block gauss seidel splittings we put forward block preconditioners which are of the product form of a scaled orthogonal matrix and a block two by two diagonal or a block two by two triangular matrix spectral distributions of these preconditioned matrices and numerical experiments show that the proposed splitting based block preconditioners can be quite competitive with the rotated block preconditioners when they are used to accelerate krylov subspace iteration methods such as gmres for solving the block two by two liner systems

an inexact relaxed dpss preconditioner for saddle point problem based on the relaxed deteriorated positive definite and skew hermitian splitting dpss preconditioner in this paper we proposed a class of relaxed deteriorated positive definite and skew hermitian splitting rdpss preconditioner for solving the saddle point problem the proposed rdpss preconditioner is a technical modification of the deteriorated positive definite and skew hermitian splitting dpss preconditioner 36 the pss preconditioner is a straightforward application of the positive definite and skew hermitian splitting pss iteration method for solving non hermitian positive definite linear systems initially established by bai et al 37 numerical results have shown that the proposed rdpss preconditioner is advantageous over the existing dpss preconditioner

block circulant preconditioners for systems arising from discretization of the three dimensional convection diffusion equation we consider the system of equations arising from finite difference discretization of a three dimensional convection diffusion model problem this system is typically nonsymmetric the gmres method with the strang block circulant preconditioner is proposed for solving this linear system we show that our preconditioners are invertible and study the spectra of the preconditioned matrices numerical results are reported to illustrate the effectiveness of our methods

structured preconditioners for nonsingular matrices of block two by two structures for the large sparse block two by two real nonsingular matrices we establish a general framework of practical and efficient structured preconditioners through matrix transformation and matrix approximations for the specific versions such as modified block jacobi type modified block gauss seidel type and modified block unsymmetric symmetric gauss seidel type preconditioners we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices also we show that when these structured preconditioners are employed to precondition the krylov subspace methods such as gmres and restarted gmres fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two by two coefficient matrices in particular these structured preconditioners can lead to efficient and high quality preconditioning matrices for some typical matrices from the real world applications

semi convergence analysis of uzawa methods for singular saddle point problems recently zheng bai and yang studied the parameterized uzawa method for solving singular saddle point problems b zheng z z bai x yang on semi convergence of parameterized uzawa methods for singular saddle point problems linear algebra appl 431 2009 808 817 in this paper we discuss the inexact uzawa method which covers the uzawa method the preconditioned uzawa method and the parameterized uzawa method to solve the singular saddle point problems we prove the semi convergence result under restrictions by verifying two necessary and sufficient conditions that is all elementary divisors associated with the eigenvalue 1 of its iterative matrix are linear and the pseudo spectral radius of the iterative matrix is less than 1 sufficient conditions for the semi convergence of several uzawa type methods are also provided in addition numerical examples are given to demonstrate the semi convergence of uzawa type methods

shift splitting preconditioners for saddle point problems in this paper we first present a shift splitting preconditioner for saddle point problems the preconditioner is based on a shift splitting of the saddle point matrix resulting in an unconditional convergent fixed point iteration based on the idea of the splitting we further propose a local shift splitting preconditioner some properties of the local shift splitting preconditioned matrix are studied these preconditioners extend those studied by bai yin and su for solving non hermitian positive definite linear systems bai et al 2006 finally numerical experiments of a model stokes problem are presented to show the effectiveness of the proposed preconditioners

a preconditioned glhss iteration method for non hermitian singular saddle point problems in this paper we propose a new preconditioned generalized local hermitian and skew hermitian splitting glhss iteration method for solving the non hermitian saddle point problems the semi convergence of this method is discussed theoretical analysis shows that the semi convergence of this new method can be guaranteed by suitable choices of the parameters and parameter matrices numerical examples are used to illustrate the theoretical results and examine the numerical effectiveness of the glhss iteration method served either as a preconditioner for gmres or as a solver

on parameterized block triangular preconditioners for generalized saddle point problems in this paper we discuss two classes of parameterized block triangular preconditioners for the generalized saddle point problems these preconditioners generalize the common block diagonal and triangular preconditioners we will give distributions of the eigenvalues of the preconditioned matrix and provide estimates for the interval containing the real eigenvalues numerical experiments of a model stokes problem are presented

a note on parameterized block triangular preconditioners for generalized saddle point problems in this paper based on the results presented by jiang et al m q jiang y cao l q yao on parameterized block triangular preconditioners for generalized saddle point problems appl math comput 216 2010 1777 1789 we consider an indefinite parameterized block triangular preconditioner for symmetric saddle point problems the eigenvalue bound of the preconditioned matrix is discussed some presented results are improved numerical experiments are given to confirm our theoretical results

performance and analysis of saddle point preconditioners for the discrete steady state navier stokes equations we examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady state navier stokes equations with a combination of analytic and empirical results we study the effects of fundamental parameters on convergence we demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers the structure of these distributions is independent of the discretization mesh size but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller these characteristics are directly correlated with the convergence properties of iterative solvers

flow induced vibrations of an elastic cylindrical shell conveying a compressible fluid abstract the paper addresses the effects of generation and transmission of the vibro acoustic energy in an elastic cylindrical shell filled with water the energy input is produced by velocity and pressure pulsations due to the presence of an obstacle in a flowing fluid it is assumed that there is no back reaction of the vibro acoustic response on the driving turbulent field the concept of modal green s functions and modal boundary integral equations is introduced and the role of elastic deformations of a tube is highlighted in view of the energy re distribution between the structural and the acoustical transmission paths another important aspect of the problem of flow induced sound generation which is addressed in this paper is the treatment of a cfd pressure output for the modelling of vibro acoustic field generation for an elastic shell in heavy fluid loading conditions it is indicated that only the pressure distribution at the surface of a shell provided by a cfd solver is requested in order to adequately predict its coupled vibro acoustic response the inner and outer acousto elastic domains are introduced and the low order system of linear algebraic equations is set up which is constituted by modal boundary equations and continuity conditions several generic excitation cases are studied and the results of analysis are explained

new variant of the hss iteration method for weighted toeplitz regularized least squares problems from image restoration abstract for fast solving weighted toeplitz least squares problems from image restoration ng and pan 2014 studied a new hermitian and skew hermitian splitting nhss preconditioner in this paper a generalization of the nhss preconditioner and the corresponding iterative method are presented convergence for the new iteration method is studied and optimal choice of the parameters is discussed bounds on the eigenvalues and the corresponding eigenvector distributions are proposed the degree of the minimal polynomial of the preconditioned matrix is obtained numerical experiments arising from image restoration are provided which show the proposed iteration method is effective and confirm our theoretical results are correct

on constraint preconditioners for generalized saddle point matrices for the iterative solution of large sparse generalized saddle point problems a class of new constraint preconditioners is presented and the spectral properties and parameter choices are discussed numerical experiments are used to demonstrate the feasibility and effectiveness of the new preconditioners as well as their advantages over the modified product type skew hermitian triangular splitting mpsts preconditioners

optimization of the parameterized uzawa preconditioners for saddle point matrices the parameterized uzawa preconditioners for saddle point problems are studied in this paper the eigenvalues of the preconditioned matrix are located in 0 2 by choosing the suitable parameters furthermore we give two strategies to optimize the rate of convergence by finding the suitable values of parameters numerical computations show that the parameterized uzawa preconditioners can lead to practical and effective preconditioned gmres methods for solving the saddle point problems

a modified product preconditioner for indefinite and asymmetric generalized saddle point matrices in this paper we present a new modified product preconditioner mp for a class of large sparse linear systems with indefinite and asymmetric matrices the eigenvalue distribution and form of the eigenvectors of the presented new preconditioned matrix and its minimal polynomial are investigated some numerical experiments illustrate that the proposed new preconditioner performs better than block diagonal preconditioner block triangular preconditioner constraint preconditioner and product preconditioner