the nsbeti method an extension of the feti method to non symmetrical bem fem coupled problems summary the finite element tearing and interconnecting feti method is recognized as an effective domain decomposition tool to achieve scalability in the solution of partitioned second order elasticity problems in the boundary element tearing and interconnecting beti method a direct extension of the feti algorithm to the bem the symmetric galerkin bem formulation is used to obtain symmetric system matrices making possible to apply the same feti conjugate gradient solver in this work we propose a new beti variant labeled nsbeti that allows to couple substructures modeled with the fem and or non symmetrical bem formulations the method connects non matching bem and fem subdomains using localized lagrange multipliers and solves the associated non symmetrical flexibility equations with a bi cgstab iterative algorithm scalability issues of nsbeti in bem bem and combined bem fem coupled problems are also investigated copyright 2012 john wiley sons ltd

error estimates in the numerical evaluation of some bem singular integrals in some applications of galerkin boundary element methods one has to compute integrals which after proper normalization are of the form b 2 x y dxdy a 1 x y y where a b 1 1 or a b a 1 or a b 1 b and f x y is a smooth function in this paper we derive error estimates for a numerical approach recently proposed to evaluate the above integral when a p or h p formulation of a galerkin method is used this approach suggests approximating the inner integral by a quadrature formula of interpolatory type that exactly integrates the cauchy kernel and the outer integral by a rule which takes into account the log endpoint singularities of its integrand some numerical examples are also given

integrable symplectic maps abstract in this paper we first give a terse survey of symplectic maps their canonical formulation and integrability then we introduce a rigorous procedure to construct integrable symplectic maps starting from integrable evolution equations on lattices a number of illustrative examples are provided

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

algebra geometric constructions of a 2 1 dimensional discrete integrable model a new 2 1 dimensional differential difference equation is considered with the aid of the nonlinearization of the lax pair the 2 1 dimensional differential difference equation is decomposed into a new integrable symplectic map and a class of finite dimensional integrable hamiltonian systems based on the theory of algebra curve the continuous flow and discrete flow are straightened out in view of the introduced abel jacobi coordinates

dual primal feti methods for three dimensional elliptic problems with heterogeneous coefficients in this paper certain iterative substructuring methods with lagrange multipliers are considered for elliptic problems in three dimensions the algorithms belong to the family of dual primal finite element tearing and interconnecting feti methods which recently have been introduced and analyzed successfully for elliptic problems in the plane the family of algorithms for three dimensions is extended and a full analysis is provided for the new algorithms particular attention is paid to finding algorithms with a small primal subspace since that subspace represents the only global part of the dual primal preconditioner it is shown that the condition numbers of several of the dual primal feti methods can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains the mesh size and jumps in the coefficients these results closely parallel those of other successful iterative substructuring methods of primal as well as dual type

associated generalized jacobi functions and polynomials abstract pointwise estimates are obtained for associated functions and polynomials corresponding to generalized jacobi weights these estimates hold uniformly in the interval of orthogonality

from the special 2 1 toda lattice to the kadomtsev petviashvili equation the nonlinearization of the eigenvalue problems associated with the toda hierarchy and the coupled korteweg de vries kdv hierarchy leads to an integrable symplectic map s and an integrable hamiltonian system h0 respectively it is proved that s and h0 have the same integrals hk the quasi periodic solution of the 2 1 dimensional kadomtsev petviashvili equation is split into three hamiltonian systems h0 h1 h2 while that of the special 2 1 dimensional toda equation is separated into h0 h1 plus the discrete flow generated by the symplectic map s a clear evolution picture of various flows is given through the window of abel jacobi coordinates the explicit theta function solutions are obtained by resorting to this separation technique

on the convergence of a dual primal substructuring method in the dual primal feti method introduced by farhat et al 1999 the domain is decomposed into non overlapping subdomains but the degrees of freedom on crosspoints remain common to all subdomains adjacent to the crosspoint the continuity of the remaining degrees of freedom on subdomain interfaces is enforced by lagrange multipliers and all degrees of freedom are eliminated the resulting dual problem is solved by preconditioned conjugate gradients we give an algebraic bound on the condition number assuming only a single inequality in discrete norms and use the algebraic bound to show that the condition number is bounded by c 1 log 2 h h for both second and fourth order elliptic selfadjoint problems discretized by conforming finite elements as well as for a wide class of finite elements for the reissner mindlin plate model

review of coupling methods for non matching meshes abstract domain decomposition is nowadays a common way to speed up complex computations however the discrete meshes used in the different domains do not have to match at their common interface especially when different physical fields are involved such as in fluid structure interaction computations exchange of information over this interface is therefore no longer trivial in this paper six methods that can deal with the information transfer between non matching meshes in fluid structure interaction computations are compared for different criteria this is done for analytical test cases as well as a quasi 1d fluid structure interaction problem two methods based on radial basis functions one with compact support and one using thin plate splines are favoured over the other methods because of their high accuracy and efficiency

a similar extension of the wki hierarchy its hamiltonian structure and the associated finite dimensional hamiltonian system abstract an isospectral problem and a similar extension of the wadati konno ichikawa hierarchy are proposed by using the trace identity it is shown that the hierarchy of equations possesses a bi hamiltonian structure the eigenvalue problem is nonlinearized to a finite dimensional hamiltonian system under a constraint between the potentials and the eigenfunctions

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 the relation of the stationary toda equation and the symplectic maps it is proved that every solution of the stationary toda equation in the generic case is represented as a discrete orbit of the symplectic map obtained through nonlinearization of the toda eigenvalue problem as an application the calculation of the finite band solution of the toda lattice equation is reduced to the solution of a system of odes plus a simple iterative process of the symplectic map

integrable semi discretization of the coupled modified kdv equations the discrete version of the inverse scattering method proposed by ablowitz and ladik is extended to solve multi component systems the extension enables one to solve the initial value problem which proves directly the complete integrability of a semi discrete version of the coupled modified korteweg de vries kdv equations and their hierarchy it also provides a procedure to obtain conservation laws and multi soliton solutions of the hierarchy

dual primal feti methods for linear elasticity dual primal feti methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations as in primal iterative substructuring methods while most of the constraints are enforced by lagrange multipliers as in one level feti methods these methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems the purpose of this article is to develop strategies for selecting these constraints which are enforced throughout the iterations such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them the algorithms are described in terms of a change of basis that has proven to be quite robust in practice a theoretical analysis is provided for the case of linear elasticity and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the young s modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain the strategies have already proven quite successful in large scale implementations of these iterative methods 2006 wiley periodicals inc

an iterative substructuring method for coupled fluid solid acoustic problems a fast parallel iterative method is proposed for the solution of linear equations arising from finite element discretization of the time harmonic coupled fluid solid systems in fluid pressure and solid displacement formulation the fluid and the solid domains are decomposed into nonoverlapping subdomains continuity of the solution is enforced by lagrange multipliers the system is augmented by duplicating the degrees of freedom on the wet interface the original degrees of freedom are then eliminated and the resulting system is solved by iterations preconditioned by a coarse space correction in each iteration the method requires the solution of one independent local acoustic problem per subdomain and the solution of a global problem with several degrees of freedom per subdomain computational results show that the method is scalable with the problem size frequency and the number of subdomains the method generalizes the feti h method for the helmholtz equation to coupled fluid elastic scattering the number of iterations is about same as for the feti h method for the related helmholtz problem with neumann boundary condition instead of an elastic scatterer if enough coarse space functions are used convergence behavior is explained from the spectrum of the iteration operator and from numerical near decoupling of the equations in the fluid and in the solid regions

a feti dp method for the parallel iterative solution of indefinite and complex valued solid and shell vibration problems the dual primal finite element tearing and interconnecting feti dp domain decomposition method ddm is extended to address the iterative solution of a class of indefinite problems of the form k 2 m u f and a class of complex problems of the form k 2 m i d u f where k m and d are three real symmetric matrices arising from the finite element discretization of solid and shell dynamic problems i is the imaginary complex number and a is a real positive number a key component of this extension is a new coarse problem based on the free space solutions of navier s equations of motion these solutions are waves and therefore the resulting ddm is reminiscent of the feti h method for this reason it is named here the feti dph method for a practically large a range feti dph is shown numerically to be scalable with respect to all of the problem size substructure size and number of substructures the cpu performance of this iterative solver is illustrated on a 40 processor computing system with the parallel solution for various a ranges of several large scale indefinite or complex valued systems of equations associated with shifted eigenvalue and forced frequency response structural dynamics problems

some new integrable systems constructed from the bi hamiltonian systems with pure differential hamiltonian operators abstract when both hamiltonian operators of a bi hamiltonian system are pure differential operators we show that the generalized kupershmidt deformation gkd developed from the kupershmidt deformation in 10 offers an useful way to construct new integrable system starting from the bi hamiltonian system we construct some new integrable systems by means of the generalized kupershmidt deformation in the cases of harry dym hierarchy classical boussinesq hierarchy and coupled kdv hierarchy we show that the gkd of harry dym equation gkd of classical boussinesq equation and gkd of coupled kdv equation are equivalent to the new integrable rosochatius deformations of these soliton equations with self consistent sources we present the lax pair for these new systems therefore the generalized kupershmidt deformation provides a new way to construct new integrable systems from bi hamiltonian systems and also offers a new approach to obtain the rosochatius deformation of soliton equation with self consistent sources

a note on a paper by g mastroianni and g monegato recently mastroianni and monegato derived error estimates for a numerical approach to evaluate the integral ab 11 f x y x y dxdy where a b 1 1 or a b a 1 or a b 1 b and f x y is a smooth function see g mastroianni and g monegato error estimates in the numerical evaluation of some bem singular integrals math comp 70 2001 251 267 the error bounds for the quadrature rule approximating the inner integral given in theorems 3 4 of that paper are not correct according to the proof however following a different approach we are able to improve the pointwise error estimates given in that paper

algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations an algebraic structure related to discrete zero curvature equations is established it is used to give an approach for generating master symmetries of the first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries the key of the theory is to generate nonisospectral flows t l l 0 from the discrete spectral problem associated with a given system of discrete evolution equations three examples are given

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

a hierarchy of coupled korteweg de vries equations and the normalisation conditions of the hilbert riemann problem the authors discuss the normalisation conditions of the hilbert riemann problem which is of importance for the construction of the ladder of soliton solutions for a given spectral problem they provide the prescription for constructing the appropriate normalisation condition all this is applied to a new hierarchy of coupled korteweg de vries equations to find the soliton solution which displays some peculiar phenomena

a parallel hp fem infrastructure for three dimensional structural acoustics this paper describes a parallel three dimensional numerical infrastructure for the solution of a wide range of time harmonic problems in structural acoustics and vibration high accuracy and rate of error convergence in the mid frequency regime is achieved by the use of hp finite and infinite element approximations the infrastructure supports parallel computation in both single and multi frequency settings multi frequency solves utilize concurrent factoring of the frequency dependent linear algebraic systems and are naturally scalable scalability of large scale single frequency problems is realized by using feti dp an iterative domain decomposition scheme numerical examples are presented to cover applications in vibratory response of fluid filled elastic structures as well as radiation and scattering from elastic structures submerged in an infinite acoustic medium we demonstrate both the numerical accuracy as well as parallel scalability of the infrastructure in terms of problem parameters that include wavenumber and number of frequencies polynomial degree of finite infinite element approximations as well as the number of processors scalability and accuracy is evaluated for both single and multiple frequency sweeps on four high performance parallel computing platforms sgi altix sgi origin ibm p690 sp and linux cluster results show good performance on shared as well as distributed memory architecture copyright 2006 john wiley sons ltd

c neumann and bargmann systems associated with the coupled kdv soliton hierarchy under two different constraints between the potentials and the eigenfunctions the eigenvalue problem associated with the coupled kdv hierarchy is nonlinearised to be a completely integrable c neumann system on the tangent bundle of sphere tsn 1 with the hamiltonian h 1 2 lambda q p 1 2 q q p p 1 2 q p 2 1 2 q p lambda p p and a completely integrable bargmann system r2n dpdq h with the hamiltonian h 1 2 lambda q p 1 2 p p q p 1 2 q q respectively the involutive solutions of the coupled kdv equation associated with the two systems are given

a new hierarchy of integrable differential difference equations and darboux transformation a new discrete isospectral problem and the corresponding hierarchy of nonlinear differential difference equations are proposed it is shown that the hierarchy of differential difference equations possesses the hamiltonian structures a darboux transformation for the discrete spectral problem is found as an application two soliton solutions for the first system of differential difference equations in the hierarchy are given

algebro geometric constructions of the discrete ablowitz ladik flows and applications resorting to the finite order expansion of the lax matrix the elliptic coordinates are introduced from which the discrete ablowitz ladik equations and the 2 1 dimensional toda lattice are decomposed into solvable ordinary differential equations the straightening out of the continuous flow and the discrete flow is exactly given through the abel jacobi coordinates as an application explicit quasiperiodic solutions for the 2 1 dimensional toda lattice are obtained

a two level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems summary we present a lagrange multiplier based two level domain decomposition method for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed method is essentially an extension of the regularized feti finite element tearing and interconnecting method to indefinite problems its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves we show numerically that the proposed method is scalable with respect to the mesh size the subdomain size and the wavenumber we report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements

on an integrable modified 2 1 dimensional lotka volterra equation in this paper an integrable 2 1 dimensional modified lotka volterra equation is considered this is a semi discrete system having discrete space and continuous time which has a known 1 1 dimensional self dual network equation as a reduction its bilinear backlund transformation and lax pair are also presented and explicit solutions including soliton solutions expressed in terms of pfaffians are obtained finally the reduction of these solutions to 1 1 dimensions is considered

integrable discretizations of derivative nonlinear schrodinger equations we propose integrable discretizations of derivative nonlinear schrodinger dnls equations such as the kaup newell equation the chen lee liu equation and the gerdjikov ivanov equation by constructing lax pairs the discrete dnls systems admit the reduction of complex conjugation between two dependent variables and possess bi hamiltonian structure through transformations of variables and reductions we obtain novel integrable discretizations of the nonlinear schrodinger nls modified kdv mkdv mixed nls matrix nls matrix kdv matrix mkdv coupled nls coupled hirota coupled sasa satsuma and burgers equations we also discuss integrable discretizations of the sine gordon equation the massive thirring model and their generalizations

a dual primal feti method for solving a class of fluid structure interaction problems in the frequency domain summary the dual primal finite element tearing and interconnecting method feti dp is extended to systems of linear equations arising from a finite element discretization for a class of fluid structure interaction problems in the frequency domain a preconditioned generalized minimal residual method is used to solve the linear equations for the lagrange multipliers introduced on the subdomain boundaries to enforce continuity of the solution the coupling between the fluid and the structure on the fluid structure interface requires an appropriate choice of coarse level degrees of freedom in the feti dp algorithm to achieve fast convergence several choices are proposed and tested by numerical experiments on three dimensional fluid structure interaction problems in the mid frequency regime that demonstrate the greatly improved performance of the proposed algorithm over the standard feti dp method copyright 2011 john wiley sons ltd

high scalable non overlapping domain decomposition method using a direct method for finite element analysis abstract in this paper a novel domain decomposition method is introduced to solve a large finite element model in this method the decomposed domains do not overlap and are connected using a simple connective finite element which influences the nodal point equilibrium between adjacent finite elements this approach has the advantage that it allows use of a direct method such as gauss elimination even in a singular problem the singular stiffness matrices from the floating domain without the dirichlet boundary conditions are changed into invertible stiffness matrices by assembling the connective elements another advantage is that computational time and storage can be reduced by using a banded matrix in the direct solver in order to describe this proposed method we first review the feti method which is the most popular domain decomposition method then the proposed method is introduced with a technical approach in a distributed computer system finally the high scalability and computational efficiency of the proposed method are verified by comparing with the traditional feti method for 2d and 3d finite element examples which have floating subdomains in the result we demonstrate high scalability for a large finite element model

a new algorithm for cauchy principal value and hadamard finite part integrals an algorithm for the approximate evaluation of integrals defined by cauchy principal value or by hadamard finite part has been proposed the convergence of the procedure is proved the stability of the algorithm is considered and some numerical examples are given