estimation for an m g queue with incomplete information summary we consider the estimation of the arrival rate and holding distribution of a discrete time queue using only information about the size of the queue arrivals are not matched to departures so that direct observations of the holding times are not available we study two estimators quickly computed moment estimators and maximum likelihood estimators based on an entropy motivated geometric approximation this approximation lends the problem a markovian structure that permits use of algorithms designed for estimating hidden markov models under the assumed model the resulting maximum likelihood estimators are efficient but the difficulty of their calculation increases exponentially with the number of parameters simulations show that the root mean squared error of maximum likeilihood estimators is about 25 smaller than that of moment estimators simulations also show how the absence of direct observations of holding times reduce the power of tests for detecting deviations from simple models

a class of parallel two level nonlinear schwarz preconditioned inexact newton algorithms we propose and test a new class of two level nonlinear additive schwarz preconditioned inexact newton algorithms aspin the two level aspin combines a local nonlinear additive schwarz preconditioner and a global linear coarse preconditioner this approach is more attractive than the two level method introduced in cai keyes and marcinkowski nonlinear additive schwarz preconditioners and applications in computational fluid dynamics international journal numerical methods in fluids 40 2002 1463 1470 which is nonlinear on both levels since the coarse part of the global function evaluation requires only the solution of a linear coarse system rather than a nonlinear coarse system derived from the discretization of original partial dierential equations the overall computational cost is reduced considerably our parallel numerical results based on an incompressible lid driven flow problem show that the new two level aspin is quite scalable with respect to the number of processors and the fine mesh size when the coarse mesh size is fine enough and in addition the convergence is not sensitive to the reynolds numbers

efficient estimation of auto regression parameters and innovation distributions for semiparametric integer valued ar p models summary integer valued auto regressive inar processes have been introduced to model non negative integer valued phenomena that evolve over time the distribution of an inar p process is essentially described by two parameters a vector of auto regression coefficients and a probability distribution on the non negative integers called an immigration or innovation distribution traditionally parametric models are considered where the innovation distribution is assumed to belong to a parametric family the paper instead considers a more realistic semiparametric inar p model where there are essentially no restrictions on the innovation distribution we provide an semiparametrically efficient estimator of both the auto regression parameters and the innovation distribution

quasi likelihood models and optimal inference consider an ergodic markov chain on the real line with parametric models for the conditional mean and variance of the transition distribution such a setting is an instance of a quasi likelihood model the customary estimator for the parameter is the maximum quasi likelihood estimator it is not efficient but as good as the best estimator that ignores the parametric model for the conditional variance we construct two efficient estimators one is a convex combination of solutions of two estimating equations the other a weighted nonlinear one step least squares estimator with weights involving predictors for the third and fourth centered conditional moments of the transition distribution additional restrictions on the model can lead to further improvement we illustrate this with an autoregressive model whose error variance is related to the autoregression parameter

robust feti dp methods for heterogeneous three dimensional elasticity problems iterative substructuring methods with lagrange multipliers are considered for heterogeneous linear elasticity problems with large discontinuities in the material stiffnesses in particular results for algorithms belonging to the family of dual primal feti methods are presented the core issue of these algorithms is the construction of an appropriate global problem in order to obtain a robust method which converges independently of the material discontinuities in this article several necessary and sufficient conditions arising from the theory are numerically tested and confirmed furthermore results of numerical experiments are presented for situations which are not covered by the theory such as curved edges and material discontinuities not aligned with the interface and an attempt is made to develop rules for these cases

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

on adaptive estimation in stationary arma processes on demontre la normalite asymptotique locale puis on construit des estimateurs localement asymptotiquement minimax

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

on the convergence of recursive trust region methods for multiscale nonlinear optimization and applications to nonlinear mechanics we prove new convergence results for a class of multiscale trust region algorithms originally introduced by gratton sartenaer and toint in siam j optim 19 2008 pp 414 444 to solve unconstrained minimization problems within the euclidean space mathbb r n we will state less restrictive assumptions on the objective function and on the iteratively computed trust region corrections which allow for proving first order convergence moreover we propose a novel projection approach for obtaining the initial coarse level iterates which are needed within the nonlinear multiscale iteration we show the efficiency and robustness of our approach by means of numerical examples from nonlinear continuum mechanics where stored energy functions for materials of ogden type and for materials with visco plastic behavior are minimized

deflation projector preconditioning and balancing in iterative substructuring methods connections and new results in this paper projector preconditioning also known as the deflation method as well as the balancing preconditioner are applied to the dual primal finite element tearing and interconnecting feti dp and balancing domain decomposition by constraints bddc methods in order to create a second independent coarse problem this may help to extend the parallel scalability of classical feti dp and bddc methods without the use of inexact solvers and may also be used to improve the robustness e g for almost incompressible elasticity problems connections of feti dp methods applying a transformation of basis using a larger coarse space with a corresponding feti dp method using projector preconditioning or balancing are pointed out it is then shown that the methods have essentially the same spectrum numerical results for compressible and almost incompressible linear elasticity are provided the sensitivity of the projection methods to an inexact computation of the projections is numerically investigated and a different behavior for projector preconditioning and the balancing preconditioner is found

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

feti dp methods with an adaptive coarse space a coarse space is constructed for the dual primal finite element tearing and interconnecting feti dp domain decomposition method applied to highly heterogeneous problems by solving local generalized eigenvalue problems for certain problems with highly varying coefficients e g from multiscale simulations the coefficient jump will appear in the condition number bound even if standard techniques such as scaling and the weighting of constraints are used the feti dp theory is revisited and two central estimates are identified where the dependency on the coefficient contrast can enter the condition number bound the first is a poincare inequality and the second an extension theorem these estimates are replaced by local eigenvalue problems enriching the feti dp coarse space by a few numerically computed eigenvectors yields independence of the contrast of the coefficients even in challenging situations

a parallel implementation of dual primal feti methods for three dimensional linear elasticity using a transformation of basis dual primal feti methods for linear elasticity problems in three dimensions are considered these are nonoverlapping domain decomposition methods where some primal continuity constraints across subdomain boundaries are required to hold throughout the iterations whereas most of the constraints are enforced by lagrange multipliers an algorithmic framework for dual primal feti methods is described together with a transformation of basis to implement the primal constraints numerical results obtained from a parallel implementation of these algorithms applied to a model benchmark problem with structured meshes and to problems with more complicated geometries from industrial and biological applications using unstructured meshes are provided these results show that the presented dual primal feti algorithms are numerical and parallel scalable

scheme of lines on a family of 2 dimensional quadrics geometry and derived category given a generic family q of 2 dimensional quadrics over a smooth 3 dimensional base y we consider the relative fano scheme m of lines of it the scheme m has a structure of a generically conic bundle m rightarrow x over a double covering x rightarrow y ramified in the degeneration locus of q rightarrow y the double covering x rightarrow y is singular in a finite number of points corresponding to the points y in y such that the quadric q y degenerates to a union of two planes the fibers of m over such points are unions of two planes intersecting in a point the main result of the paper is a construction of a semiorthogonal decomposition for the derived category of coherent sheaves on m this decomposition has three components the first is the derived category of a small resolution x of singularities of the double covering x rightarrow y the second is a twisted resolution of singularities of x given by the sheaf of even parts of clifford algebras on y and the third is generated by a completely orthogonal exceptional collection

optimal convergence properties of the feti domain decomposition method abstract the finite element tearing and interconnecting feti method is a practical and efficient domain decomposition dd algorithm for the solution of self adjoint elliptic partial differential equations for large scale structural problems discretized with shell and beam elements this method was found to outperform popular iterative algorithms and direct solvers on both serial and parallel computers and to compare favorably with leading dd methods in this paper we discuss some numerical properties of the feti method that were not addressed before in particular we show that the mathematical treatment of the floating subdomains and the specific conjugate projected gradient algorithm that characterize the feti method are equivalent to the construction and solution of a coarse problem that propagates the error globally accelerates convergence and ensures a performance that is independent of the number of subdomains we also show that when the interface problem is optimally preconditioned and the mesh is partitioned into well structured subdomains with good aspect ratios the performance of the feti method is also independent of the mesh size however we also argue that the feti and other leading dd methods for unstructured problems lose in practice these scalability properties when the mesh contains junctures with rotational degrees of freedom or the decomposition is irregular and characterized by arbitrary subdomain aspect ratios finally we report that for realistic problems optimal preconditioners are not necessarily computationally efficient and can be outperformed by non optimal ones

a scalable substructuring method by lagrange multipliers for plate bending problems we present a new lagrange multiplier based domain decomposition method for solving iteratively systems of equations arising from the finite element discretization of plate bending problems the proposed method is essentially an extension of the finite element tearing and interconnecting substructuring algorithm to the biharmonic equation the main idea is to enforce continuity of the transversal displacement field at the subdomain crosspoints throughout the preconditioned conjugate gradient iterations the resulting method is proved to have a condition number that does not grow with the number of subdomains but rather grows at most polylogarithmically with the number of elements per subdomain these optimal properties hold for numerous plate bending elements that are used in practice including the hsieh clough tocher element the discrete kirchhoff triangle and a class of nonlocking elements for the reissner mindlin plate models computational experiments are reported and shown to confirm the theoretical optimal convergence properties of the new domain decomposition method computational efficiency is also demonstrated with the numerical solution in 45 iterations and 105 seconds on a 64 processor ibm sp2 of a plate bending problem with almost one million degrees of freedom

nonlinear localization strategies for domain decomposition methods application to post buckling analyses abstract in this paper we explore the capabilities of some nonlinear strategies based on domain decomposition for nonlinear analyses and more particularly for post buckling analyses of large slender structures after having recalled the classical newton krylov schur methods chosen here to serve as a reference we propose two versions specifically developed to treat nonlinear phenomena at the most relevant scale through nonlinear localizations per substructure all these different strategies lead to solving similar condensed problems on which we apply classical domain decomposition methods performances are discussed and comparative results in terms of convergence are presented in the case of beam frames with large rotations and local buckling

mixed inar 1 poisson regression models analyzing heterogeneity and serial dependencies in longitudinal count data this paper presents finite mixture versions of integer valued autoregressive inar poisson regression models for investigating regularity and predictability of purchase behavior over time the approach facilitates the analysis of heterogeneity and serial correlation effects as well as conditional and marginal analyses of the effects of covariates an application to scanner panel data of detergents yields substantive insights into sources of autodependencies in individual category purchases

parallelization of continuous and discontinuous galerkin dual primal isogeometric tearing and interconnecting methods abstract in this paper we investigate the parallelization of dual primal isogeometric tearing and interconnecting ieti dp type methods for solving large scale continuous and discontinuous galerkin systems of equations arising from isogeometric analysis of elliptic boundary value problems these methods are extensions of the finite element tearing and interconnecting methods to isogeometric analysis the algorithms are implemented by means of energy minimizing primal subspaces we discuss how these methods can efficiently be parallelized in a distributed memory setting weak and strong scaling studies presented for two and three dimensional problems show an excellent parallel efficiency

derived categories of quadric fibrations and intersections of quadrics abstract we construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of the fibration and the derived category of coherent sheaves of modules over the sheaf of even parts of the clifford algebras on the base corresponding to this quadric fibration generalizing the kapranov s description of the derived category of a single quadric as an application we verify that the noncommutative algebraic variety p s 2 w b 0 where b 0 is the universal sheaf of even parts of clifford algebras is homologically projectively dual to the projective space p w in the double veronese embedding p w p s 2 w using the properties of the homological projective duality we obtain a description of the derived category of coherent sheaves on a complete intersection of any number of quadrics

the approximate component mode synthesis special finite element method in two dimensions a special finite element method based on approximate component mode synthesis acms was introduced in hetmaniuk and lehoucq 2010 acms was developed for second order elliptic partial differential equations with rough or highly varying coefficients here a parallel implementation of acms is presented and parallel scalability issues are discussed for representative examples additionally a parallel domain decomposition preconditioner feti dp is applied to solve the acms finite element system weak parallel scalability results for acms are presented for up to 1024 cores our numerical results also suggest a quadratic logarithmic condition number bound for the preconditioned feti dp method applied to acms discretizations

adaptive selection of face coarse degrees of freedom in the bddc and the feti dp iterative substructuring methods we propose a class of method for the adaptive selection of the coarse space of the bddc and feti dp iterative substructuring methods the methods work by adding coarse degrees of freedom constructed from eigenvectors associated with intersections of selected pairs of adjacent substructures it is assumed that the starting coarse degrees of freedom are already sufficientto prevent relative rigid body motions in any selected pair of adjacent substructures a heuristic indicator of the the condition number is developed and a minimal number of coarse degrees of freedom is added to decrease the indicator under a given threshold it is shown numerically on 2d elasticity problems that the indicator based on pairs of substructures with common edges predicts the actual condition number reasonably well and that the method can select adaptively the hard part of the problem and concentrate computational work there to achieve good convergence of the iterations at a modest cost

nonlinear feti dp and bddc methods new nonlinear feti dp dual primal finite element tearing and interconnecting and bddc balancing domain decomposition by constraints domain decomposition methods are introduced in all these methods in each iteration local nonlinear problems are solved on the subdomains the new approaches can significantly reduce communication and show a significantly improved performance especially for problems with localized nonlinearities compared to a standard newton krylov feti dp or bddc approach moreover the coarse space of the nonlinear feti dp methods can be used to accelerate the newton convergence it is also found that the new nonlinear feti dp and nonlinear bddc methods are not as closely related as in the linear context numerical results for the p laplace operator are presented

on nodal enriques surfaces and quartic double solids we consider the class of singular double coverings x rightarrow mathbb p 3 ramified in the degeneration locus d of a family of 2 dimensional quadrics these are precisely the quartic double solids constructed by artin and mumford as examples of unirational but nonrational conic bundles with such a quartic surface d one can associate an enriques surface s which is the factor of the blowup of d by a natural involution acting without fixed points such enriques surfaces are known as nodal enriques surfaces or reye congruences we show that the nontrivial part of the derived category of coherent sheaves on this enriques surface s is equivalent to the nontrivial part of the derived category of a minimal resolution of singularities of x

toward extremely scalable nonlinear domain decomposition methods for elliptic partial differential equations the solution of nonlinear problems e g in material science requires fast and highly scalable parallel solvers finite element tearing and interconnecting dual primal feti dp domain decomposition methods are parallel solution methods for implicit problems discretized by finite elements recently nonlinear versions of the well known feti dp methods for linear problems have been introduced in these methods the nonlinear problem is decomposed before linearization this approach can be viewed as a strategy to further localize computational work and to extend the parallel scalability of feti dp methods toward extreme scale supercomputers here a recent nonlinear feti dp method is combined with an approach that allows an inexact solution of the feti dp coarse problem we combine the nonlinear feti dp domain decomposition method with an algebraic multigrid amg method and thus obtain a hybrid nonlinear domain decomposition multigrid method we consider scalar nonlinear problems as well as nonlinear hyp

abstract robust coarse spaces for systems of pdes via generalized eigenproblems in the overlaps coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations pdes however it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the pde coefficients especially for systems of pdes here we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities we achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence we prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous pdes and systems of pdes that confirm this property

feti and neumann neumann iterative substructuring methods connections and new results the feti and neumann neumann families of algorithms are among the best know and most severely tested domain decomposition methods for elliptic partial differential equations they are iterative substructuring methods and have many algorithmic components in common but there are also differences the purpose of this paper is to further unify the theory for these two families of methods and to introduce a new family of feti algorithms bounds on the rate of convergence which are uniform with respect to the coefficients of a family of elliptic problems with heterogeneous coefficients are established for these new algorithms the theory for a variant of the neumann neumann algorithm is also redeveloped stressing similarities to that for the feti methods

extending substructure based iterative solvers to multiple load and repeated analyses direct solvers currently dominate commercial finite element structural software but do not scale well in the fine granularity regime targeted by emerging parallel processors substructure based iterative solvers often called also domain decomposition algorithms lend themselves better to parallel processing but must overcome several obstacles before earning their place in general purpose structural analysis programs one such obstacle is the solution of systems with many or repeated right hand sides such systems arise for example in multiple load static analyses and in implicit linear dynamics computations direct solvers are well suited for these problems because after the system matrix has been factored the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions on the other hand iterative solvers in general are ill suited for these problems because they often must restart from scratch for every different right hand side in this paper we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides basically we formulate the overall problem as a series of minimization problems over k orthogonal and supplementary subspaces and tailor the preconditioned conjugate gradient algorithm to solve them efficiently the resulting solution method is scalable whereas direct factorization schemes and forward and backward substitution algorithms are not we illustrate the proposed methodology with the solution of static and dynamic structural problems and highlight its potential to outperform forward and backward substitutions on parallel computers as an example we show that for a linear structural dynamics problem with 11640 degrees of freedom every time step beyond time step 15 is solved in a single iteration and consumes 1 0 second on a 32 processor ipsc 860 system for the same problem and the same parallel processor a pair of forward backward substitutions at each step consumes 15 0 seconds

incorporation of linear multipoint constraints in substructure based iterative solvers part 1 a numerically scalable algorithm we consider the iterative solution by a class of substructuring methods of the large scale systems of equations arising from the nite element discretization of structural models with an arbitrary set of linear multipoint constraints we present a methodology for generalizing to such problems numerically scalable substructure based iterative solvers without interfering with their formulations and their well established local and global preconditioners we apply this methodology to the feti method and show that the resulting algorithm is numerically scalable with respect to both the substructure and problem sizes 1998 john wiley sons ltd

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

nonlinear parallel in time schur complement solvers for ordinary differential equations abstract in this work we propose a parallel in time solver for linear and nonlinear ordinary differential equations the approach is based on an efficient multilevel solver of the schur complement related to a multilevel time partition for linear problems the scheme leads to a fast direct method next two different strategies for solving nonlinear odes are proposed first we consider a newton method over the global nonlinear ode using the multilevel schur complement solver at every nonlinear iteration second we state the global nonlinear problem in terms of the nonlinear schur complement at an arbitrary level and perform nonlinear iterations over it numerical experiments show that the proposed schemes are weakly scalable i e we can efficiently exploit increasing computational resources to solve for more time steps the same problem

newton krylov bddc solvers for nonlinear cardiac mechanics abstract the aim of this work is to design and study a balancing domain decomposition by constraints bddc solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue the contraction relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro mechanical models consisting of systems of partial and ordinary differential equations in this study the discretization of the electro mechanical models is performed by q1 finite elements in space and semi implicit finite difference schemes in time leading to the solution of a large scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation the parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a newton krylov bddc method based on the parallel solution of local mechanical problems and a coarse problem for the so called primal unknowns three dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains quasi optimal in the ratio of subdomain to mesh sizes and robust with respect to tissue anisotropy

the two level feti method for static and dynamic plate problems part i an optimal iterative solver for biharmonic systems abstract we present a lagrange multiplier based substructuring method for solving iteratively large scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems the proposed method is essentially an extension of the feti domain decomposition algorithm to fourth order problems the main idea is to enforce exactly the continuity of the transverse displacement field at the substructure corners throughout the preconditioned conjugate projected gradient iterations this results in a two level feti substructuring method where the condition number of the preconditioned interface problem does not grow with the number of substructures and grows at most polylogarithmically with the number of elements per substructure these theoretically proven optimal convergence properties of the new feti method are numerically demonstrated for several finite element plate bending static and transient problems the two level iterative solver presented in this paper is applicable to a large family of biharmonic time independent as well as time dependent systems it is also extendible to shell problems

spectral element feti dp and bddc preconditioners with multi element subdomains abstract the discrete systems generated by spectral or hp version finite elements are much more ill conditioned than the ones generated by standard low order finite elements or finite differences this paper focuses on spectral elements based on gauss lobatto legendre gll quadrature and the construction of primal and dual non overlapping domain decomposition methods belonging to the family of balancing domain decomposition methods by constraints bddc and dual primal finite element tearing and interconnecting feti dp algorithms new results are presented for the spectral multi element case and also for inexact feti dp methods for spectral elements in the plane theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator while there is only a polylogarithmic dependence on the spectral degree p and the ratio h h of subdomain and element sizes parallel numerical experiments on a linux cluster confirm these results for tests with spectral degree up to p 32 thousands of subdomains and coefficient jumps up to 8 orders of magnitude

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

double covers of quadratic degeneracy and lagrangian intersection loci we explain a general construction of double covers of quadratic degeneracy loci and lagrangian intersection loci based on reflexive sheaves we relate the double covers of quadratic degeneracy loci to the stein factorizations of the relative hilbert schemes of linear spaces of the corresponding quadric fibrations we give a criterion for these double covers to be nonsingular these results are an extension of o grady s construction of double covers of epw sextics and provide an alternate construction of iliev kapustka kapustka ranestad s epw cubes

an inar 1 negative multinomial regression model for longitudinal count data this paper discusses a regression model for the analysis of longitudinal count data observed in a panel study an integer valued first order autoregressive inar 1 poisson process is adapted to represent time dependent correlations among the counts by combining the inar 1 representation with a random effects approach a new negative multinomial distribution is derived that includes the bivariate negative binomial distribution proposed by edwards and gurland 1961 and subrahmaniam 1966 as a special case a detailed analysis of the relationship between personality factors and daily emotion experiences illustrates the approach

the second generation feti methods and their application to the parallel solution of large scale linear and geometrically non linear structural analysis problems the feti algorithms are a family of numerically scalable domain decomposition methods they have been designed in the early 1990s for solving iteratively and on parallel machines large scale systems of equations arising from the finite element discretization of solid mechanics structural engineering structural dynamics and acoustic scattering problems and for analyzing complex structures obtained from the assembly of substructures with incompatible discrete interfaces in this paper we present the second generation of these methods that operate more efficiently on large numbers of subdomains offer greater robustness better performance and more flexibility for implementation on a wider variety of computational platforms we also report on the application and performance of these methods for the solution of geometrically non linear structural analysis problems we discuss key aspects of their implementation on shared and distributed memory parallel processors benchmark them against optimized direct sparse solvers and highlight their potential with the solution of large scale structural mechanics problems with several million degrees of freedom

nonlinear feti dp and bddc methods a unified framework and parallel results parallel newton krylov feti dp finite element tearing and interconnecting dual primal domain decomposition methods are fast and robust solvers e g for nonlinear implicit problems in structural mechanics in these methods the nonlinear problem is first linearized and then decomposed into loosely coupled linear problems which can be solved in parallel by changing the order of the operations new parallel communication can be constructed where the loosely coupled local problems are nonlinear we discuss different nonlinear feti dp methods which are equivalent when applied to linear problems but which show a different performance for nonlinear problems moreover a new unified framework is introduced which casts all nonlinear feti dp domain decomposition approaches discussed in the literature into a single algorithm furthermore the equivalence of nonlinear feti dp methods to specific nonlinearly right preconditioned newton krylov methods is shown for the methods using nested newton iteration

derived equivalent calabi yau threefolds from cubic fourfolds we describe pretty examples of derived equivalences and autoequivalences of calabi yau threefolds arising from pencils of cubic fourfolds the cubic fourfolds are chosen to be special so they each have an associated k3 surface thus a pencil gives rise to two different calabi yau threefolds the associated pencil of k3 surfaces and the baselocus of the original pencil the intersection of two cubic fourfolds they both have crepant resolutions which are derived equivalent

a scalable lagrange multiplier based domain decomposition method for time dependent problems we present a new efficient and scalable domain decomposition method for solving implicitly linear and non linear time dependent problems in computational mechanics the method is derived by adding a coarse problem to the recently proposed transient feti substructuring algorithm in order to propagate the error globally and accelerate convergence it is proved that in the limit for large time steps the new method converges toward the feti algorithm for time independent problems computational results confirm that the optimal convergence properties of the time independent feti method are preserved in the time dependent case we employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors and demonstrate the effective scalability of the new transient feti method with the large scale finite element dynamic analysis on the paragon xp s and ibm sp2 systems of several diffraction grating finite element structural models we also show that this new domain decomposition method outperforms the popular direct skyline solver the coarse problem presented herein is applicable and beneficial to a large class of lagrange multiplier based substructuring algorithms for time dependent problems including the fictitious domain decomposition method

schwarz methods of neumann neumann type for three dimensional elliptic finite element problems several domain decomposition methods of neumann neumann type are considered for solving the large linear systems of algebraic equations that arise from discretizations of elliptic problems by finite elements we will only consider problems in three dimensions several new variants of the basic algorithm are introduced in a schwarz method framework that provides tools which have already proven very useful in the design and analysis of other domain decomposition and multi level methods the neumann neumann algorithms have several advantages over other domain decomposition methods the subregions which define the subproblems only share the boundary degrees of freedom with their neighbors the subregions can also be of quite arbitrary shape and many of the major components of the preconditioner can be constructed from subprograms available in standard finite element program libraries in its original form however the algorithm lacks a mechanism for global transportation of information and its performance therefore suffers when the number of subregions increases in the new variants of the algorithms considered in this paper the preconditioners include global components of low rank to overcome this difficulty bounds are established for the condition number of the iteration operator which are independent of the number of subregions and depend only polylogarithmically on the number of degrees of freedom of individual local subproblems results are also given for problems with arbitrarily large jumps in the coefficients across the interfaces separating the subregions 1995 john wiley sons inc

on clifford double mirrors of toric complete intersections abstract we present a construction of noncommutative double mirrors to complete intersections in toric varieties this construction unifies existing sporadic examples and explains the underlying combinatorial and physical reasons for their existence

efficient probabilistic forecasts for counts summary efficient probabilistic forecasts of integer valued random variables are derived the optimality is achieved by estimating the forecast distribution non parametrically over a given broad model class and proving asymptotic non parametric efficiency in that setting the method is developed within the context of the integer auto regressive class of models which is a suitable class for any count data that can be interpreted as a queue stock birth and death process or branching process the theoretical proofs of asymptotic efficiency are supplemented by simulation results that demonstrate the overall superiority of the non parametric estimator relative to a misspecified parametric alternative in large but finite samples the method is applied to counts of stock market iceberg orders a subsampling method is used to assess sampling variation in the full estimated forecast distribution and a proof of its validity is given

a nonlinear elimination preconditioned inexact newton method for heterogeneous hyperelasticity we propose and study a nonlinear elimination preconditioned inexact newton method for the numerical simulation of diseased human arteries with a heterogeneous hyperelastic model we assume the arte

likelihood estimation for the inar p model by saddlepoint approximation saddlepoint techniques have been used successfully in many applications owing to the high accuracy with which they can approximate intractable densities and tail probabilities this article concerns their use for the estimation of high order integer valued autoregressive inar p processes conditional least squares estimation and maximum likelihood estimation have been proposed for inar p models but the first is inefficient for estimating parametric models and the second becomes difficult to implement as the order p increases we propose a simple saddlepoint approximation to the log likelihood that performs well even in the tails of the distribution and with complicated inar models we consider poisson and negative binomial innovations and show empirically that the estimator that maximises the saddlepoint approximation behaves very similarly to the maximum likelihood estimator in realistic settings the approach is applied to data on meningococcal disease counts supplementary materials for this ar

on the general solution by a direct method of a large scale singular system of linear equations application to the analysis of floating structures finding the general solution of a singular system of linear equations requires computing a particular solution and a basis of the null space of the corresponding singular matrix in this paper we consider the case where the singular matrix is large and sparse and the application calls for a direct solution method we highlight the dependence of straightforward factorization algorithms on an arbitrary constant that can influence the correctness of the computed solution and describe a family of improved direct solution methods that alleviate this problem for structural mechanics applications we propose a hybrid geometric algebraic method that is more robust than the purely algebraic direct methods that are currently used for solving singular sparse systems of equations we illustrate the potential of our proposed solution algorithms with examples from structural mechanics and domain decomposition based iterative solvers 1998 john wiley sons ltd

convergence of a substructuring method with lagrange multipliers we analyze the convergence of a substructing iterative method with lagrange multipliers propose recently by farhat and roux the method decomposes finite element discretization of an elliptic boundary value problem into neumann problems on the subdomains plus a coarse problem for the subdomain nullspace components for linear conforming elements and preconditioning by the dirichlet problems on the subdomains we prove the asymptotic bound on the condition number c 1 log h h alpha alpha 2 or 3 where h is the characteristic element size h subdomain size and c is independent of the number of subdomains

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models