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

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

controlled differential equations as young integrals a simple approach the theory of rough paths allows one to define controlled differential equations driven by a path which is irregular the most simple case is the one where the driving path has finite p variations with 1 p 2 in which case the integrals are interpreted as young integrals the prototypal example is given by stochastic differential equations driven by fractional brownian motion with hurst index greater than 1 2 using simple computations we give the main results regarding this theory existence uniqueness convergence of the euler scheme flow property which are spread out among several articles

incorporation of linear multipoint constraints in domain decomposition based iterative solvers part ii blending feti dp and mortar methods and assembling floating substructures two approaches are presented for extending the feti dp domain decomposition based iterative method to the solution of problems with linear multipoint constraints lmpcs both cases of arbitrary lmpcs and lmpcs generated by the mortar method for enforcing a weak continuity of the solution across non matching finite element interfaces are considered in the first approach the lmpcs are addressed during the preconditioning step but enforced only at convergence in the second approach the lmpcs are enforced at each iteration through the solution of an auxiliary coarse problem both extended feti dp solvers are benchmarked on a parallel processor for a wide range of constrained structural mechanics problems the obtained results reveal that both solvers are numerically scalable and complement each other from the memory and cpu performance viewpoints

a two step two field hybrid method for the static and dynamic analysis of substructure problems with conforming and non conforming interfaces abstract the need for assembling independent finite element substructure solutions arises in several engineering and scientific problems including the design and analysis of complex structural systems component mode synthesis global local analysis adaptive refinement and parallel processing in this paper we discuss the solution of such problems by a two field hybrid method where the substructures are jointed with low order polynomial or piece wise polynomial lagrange multipliers and present a rayleigh ritz based smoothing procedure for improving the accuracy of the computed coupled solution in the presence of various substructure heterogeneities we consider both conforming and nonconforming substructure meshes and demonstrate the benefits of the proposed two step solution method with several examples from structural mechanics

the dual schur complement method with well posed local neumann problems regularization with a perturbed lagrangian formulation the dual schur complement dsc domain decomposition dd method introduced by farhat and roux is an efficient and practical algorithm for the parallel solution of self adjoint elliptic partial dif

variational solutions for partial differential equations driven by a fractional noise abstract in this article we develop an existence and uniqueness theory of variational solutions for a class of nonautonomous stochastic partial differential equations of parabolic type defined on a bounded open subset d r d and driven by an infinite dimensional multiplicative fractional noise we introduce two notions of such solutions for them and prove their existence and their indistinguishability by assuming that the noise is derived from an l 2 d valued fractional wiener process w h with hurst parameter h 1 1 1 whose covariance operator satisfies appropriate integrability conditions and where 0 1 denotes the holder exponent of the derivative of the nonlinearity in the stochastic term of the equations we also prove the uniqueness of solutions when the stochastic term is an affine function of the unknown random field our existence and uniqueness proofs rest upon the construction and the convergence of a suitable sequence of faedo galerkin approximations while our proof of indistinguishability is based on certain density arguments as well as on new continuity properties of the stochastic integral we define with respect to w h

controlling rough paths abstract we formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints this allows us to define a good notion of integral with respect to irregular paths with holder exponent greater than 1 3 e g samples of brownian motion and study the problem of the existence uniqueness and continuity of solution of differential equations driven by such paths we recover young s theory of integration and the main results of lyons theory of rough paths in holder topology

positive periodic solutions of discrete three level food chain model of holling type ii with the help of differential equations with piecewise constant arguments we first derive a discrete analogy of continuous three level food chain model of holling type ii which is governed by difference equations with periodic coefficients a set of sufficient conditions is derived for the existence of positive periodic solutions with strictly positive components by using the continuation theorem in coincidence degree theory particularly the upper and lower bounds of the periodic solutions are also established

extended preconditioners for the feti method applied to constrained problems an efficient and simple approach for handling linear multipoint constraints in a class of substructure based solvers namely the finite element tearing and interconnecting feti method is proposed previously it was argued that multipoint constraints should be handled in feti by adding a second level iteration on a coarse grid such that the feti iterates satisfy the multipoint constraints exactly the procedure presented here does not require an additional coarse grid but instead takes account of the multipoint constraints in the preconditioning step the preconditioning strategy is shown to be mechanically consistent and to incur only a small additional computational cost this strategy is simpler and computationally less expensive than the two level feti procedure its numerical scalability even for highly heterogeneous problems is demonstrated in several test examples

a new dual mortar method for curved interfaces 2d elasticity dual mortar method formulations have shown to be a very effective and efficient way for interfacing e g tying contacting dissimilar meshes on the other hand we have recently found that they can sometimes perform quite poorly when applied to curved surfaces in some solid mechanics applications a new modified two dimensional dual mortar method for piecewise linear finite elements is developed that overcomes this deficiency and is demonstrated on a model problem furthermore mathematical analysis is provided to demonstrate the optimal convergence and stability of the new method copyright 2005 john wiley sons ltd

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

the specified boundary stiffness force sbsf method for finite element subregion analysis it is difficult to analyse a large complex structure in sufficient detail to obtain accurate results everywhere one approach is simply to refine the whole structure model in the regions of interest another approach is to identify a subregion of the structure and develop a separate refined model of the subregion it is difficult to assure accuracy in this subregion model because of uncertainties in specifying boundary conditions and loading from the whole structure model solution in the current literature three methods other than whole model refinement have been described to deal with this problem these are called the specified boundary displacement method the linear constraint method and the zooming method this paper describes a new approach to this problem of modelling subregions this approach uses the stiffnesses and forces from the whole model solution at the nodes on the boundary of the sub region model accurate displacement and stress solutions are obtained with this method as it takes into account the interaction between the new stiffness of the subregion and the rest of the structure this approach is similar to substructuring however the equations outside the subregion are discarded rather than condensed out which results in much less computation effort examples of the application of this method to the problem of a plate with a centre hole in tensile loading are presented the results compared favourably with the results of the same problem solved using other methods with significant improvement in accuracy over the specified boundary displacement method also presented are some results from design modification of the subregion which illustrate the potential of this method for redesign application

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

pade approximants and the modal connection towards increased robustness for fast parametric sweeps summary in order to increase the robustness of a pade based approximation of parametric solutions to finite element problems an a priori estimate of the poles is proposed the resulting original approach is shown to allow for a straightforward efficient subsequent pade based expansion of the solution vector components overcoming some of the current convergence and robustness limitations in particular this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of pade approximants the choice of these approximants as shown in the present work is theoretically supported by the montessus de ballore theorem concerning the convergence of a series of approximants with fixed denominator degrees key features and originality of the proposed approach are i a component wise expansion which allows to specifically target subsets of the solution field and ii the a priori simultaneous choice of the pade approximants and their associated interval of convergence for an effective and more robust approximation an academic acoustic case study a structural acoustic application and a larger acoustic problem are presented in order to demonstrate the potential of the approach proposed this article is protected by copyright all rights reserved

rough differential equations driven by signals in besov spaces rough differential equations are solved for signals in general besov spaces unifying in particular the known results in holder and p variation topology to this end the paracontrolled distribution approach which has been introduced by gubinelli imkeller and perkowski 24 to analyze singular stochastic pdes is extended from holder to besov spaces as an application we solve stochastic differential equations driven by random functions in besov spaces and gaussian processes in a pathwise sense

a simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems several domain decomposition methods with lagrange multipliers have been recently designed for solving iteratively large scale systems of finite element equations while these methods differ typically by implementational details they share in most cases the same substructure based preconditioners that were originally developed for the feti method the success of these preconditioners is due to the fact that for homogeneous structural mechanics problems they ensure a computational performance that scales with the problem size in this paper we address the suboptimal behaviour of these preconditioners in the presence of material and or discretization heterogeneities we propose a simple and virtually no cost extension of these preconditioners that exhibits scalability even for highly heterogeneous systems of equations we consider several intricate structural analysis problems and demonstrate numerically the optimal performance delivered by the new preconditioners for problems with discontinuities copyright 1999 john wiley sons ltd

a version of hormander s theorem for the fractional brownian motion it is shown that the law of an sde driven by fractional brownian motion with hurst parameter greater than 1 2 has a smooth density with respect to lebesgue measure provided that the driving vector fields satisfy hormander s condition the main new ingredient of the proof is an extension of norris lemma to this situation

on the l2 and the h1 couplings for an overlapping domain decomposition method using lagrange multipliers in this paper a comparison of the l 2 and the h couplings is made for an overlapping domain decomposition method using lagrange multipliers the analysis of the local equations arising from the formulation of the coupling of two mechanical models shows that continuous weight functions are required for the l 2 coupling term whereas both discontinuous and continuous weight functions can be used for the h 1 coupling the choice of the lagrange multiplier space is discussed and numerically studied the paper ends with some numerical examples of an end loaded cantilever beam and a cracked plate under tension and shear it is shown that the continuity enforced with the h 1 coupling leads to a link with a flexibility that can be beneficial for coupling a very coarse mesh with a very fine one to limit the effect of the volume coupling on the global response a narrow coupling zone is recommended in this case volume coupling tends to a surface coupling especially with a l 2 coupling

consistent mesh tying methods for topologically distinct discretized surfaces in non linear solid mechanics this work presents a new technique for joining dissimilar meshes in non linear finite element analysis with the novel result that the adjoining surfaces do not need to be spatially coincident for patch tests to be passed the work builds in some sense on results previously presented by dohrmann et al international journal for numerical methods in engineering 1991 40 1205 but considerably generalizes upon the results presented there most importantly it is shown that consistency of the tied finite element formulation may be achieved such that implementation of element formulations is not affected through the use of a three field variational principle applied over the contacting region a key conclusion of the work is that although the approach advocated bears some resemblance to mortar element schemes for contact analysis see for example mcdevitt and laursen international journal for numerical methods in engineering 2000 48 1525 a straightforward application of a mortaring scheme is not sufficient to guarantee patch test passage when dissimilar meshing of curved surfaces leads to local open volumes or overlaps between tied surfaces in their reference configurations the proposed algorithm is demonstrated through a number of numerical examples performed within a matrix free non linear equation solving framework published in 2003 by john wiley sons ltd

hopf bifurcation and stability analysis in a harvested one predator two prey model in this paper hopf bifurcation is demonstrated in an interacting one predator two prey model with harvesting of the predator at a constant rate here harvest rate is used as a control parameter it is found that periodic solutions arise from stable stationary states when the harvest rate exceeds a certain limit the stability of these periodic solutions is investigated with the variation of this control parameter the approach is analytic in nature and the normal form analysis of the model is performed

sensitivity of rough differential equations an approach through the omega lemma the ito map assigns the solution of a rough differential equation a generalization of an ordinary differential equation driven by an irregular path when existence and uniqueness hold by studying how a path is transformed through the vector field which is integrated we prove that the ito map is holder or lipschitz continuous with respect to all its parameters this result unifies and weaken the hypotheses of the regularity results already established in the literature