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1.
    
A unified framework of dual‐primal finite element tearing and interconnecting (FETI‐DP) algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equations. A distinctive feature of this framework is that it allows using both continuous and discontinuous pressures in the algorithm, whereas previous FETI‐DP methods only apply to discontinuous pressures. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved. This framework is also used to describe several previously developed FETI‐DP algorithms and greatly simplifies their analysis. Numerical experiments of solving a two‐dimensional incompressible Stokes problem demonstrate the performances of the discussed FETI‐DP algorithms represented under the same framework.Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

2.
    
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 ?σ2 M ) u = f , and a class of complex problems of the form ( K ?σ2 M +iσ 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 σ 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 σ 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 σ ranges, of several large‐scale, indefinite, or complex‐valued systems of equations associated with shifted eigenvalue and forced frequency response structural dynamics problems. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

3.
    
As parallel and distributed computing gradually becomes the computing standard for large scale problems, the domain decomposition method (DD) has received growing attention since it provides a natural basis for splitting a large problem into many small problems, which can be submitted to individual computing nodes and processed in a parallel fashion. This approach not only provides a method to solve large scale problems that are not solvable on a single computer by using direct sparse solvers but also gives a flexible solution to deal with large scale problems with localized non‐linearities. When some parts of the structure are modified, only the corresponding subdomains and the interface equation that connects all the subdomains need to be recomputed. In this paper, the dual–primal finite element tearing and interconnecting method (FETI‐DP) is carefully investigated, and a reduced back‐substitution (RBS) algorithm is proposed to accelerate the time‐consuming preconditioned conjugate gradient (PCG) iterations involved in the interface problems. Linear–non‐linear analysis (LNA) is also adopted for large scale problems with localized non‐linearities based on subdomain linear–non‐linear identification criteria. This combined approach is named as the FETI‐DP‐RBS‐LNA algorithm and demonstrated on the mechanical analyses of a welding problem. Serial CPU costs of this algorithm are measured at each solution stage and compared with that from the IBM Watson direct sparse solver and the FETI‐DP method. The results demonstrate the effectiveness of the proposed computational approach for simulating welding problems, which is representative of a large class of three‐dimensional large scale problems with localized non‐linearities. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

4.
    
This paper investigates the question of the building of admissible stress field in a substructured context. More precisely, we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), and (3) a procedure to build admissible fields for dual‐primal finite element tearing and interconnecting and balancing domain decomposition by constraints methods leading to an error bound that separates the contributions of the solver and of the discretization. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
    
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.  相似文献   

6.
We present a domain decomposition method with Lagrange multipliers for solving iteratively frictionless contact problems. This method, which is based on the FETI method and therefore is named here the FETI‐C method, incorporates a coarse contact system that guides the iterative prediction of the active zone of contact. We demonstrate numerically that this method is numerically scalable with respect to both the problem size and the number of subdomains. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

7.
    
We present a method with domain decomposition to solve time‐dependent non‐linear problems. This method enables arbitrary numeric schemes of the Newmark family to be coupled with different time steps in each subdomain: this coupling is achieved by prescribing continuity of velocities at the interface. We are more specifically interested in the coupling of implicit/explicit numeric schemes taking into account material and geometric non‐linearities. The interfaces are modelled using a dual Schur formulation where the Lagrange multipliers represent the interfacial forces. Unlike the continuous formulation, the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements, velocities and accelerations at the interfaces. We show that, within the framework of the Newmark family of numeric schemes, continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged. To prove this stability, we use an energy method, i.e. a global method over the whole time interval, in order to verify the algorithms properties. Then, we propose to extend this to non‐linear situations in the following cases: implicit linear/explicit non‐linear, explicit non‐linear/explicit non‐linear and implicit non‐linear/explicit non‐linear. Finally, we present some examples showing the feasibility of the method. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

8.
    
In this paper, we introduce a two‐scale diffusion–deformation coupled model that represents the aging material deterioration of two‐phase materials involving micro‐crack propagations. The mathematical homogenization method is applied to relate the micro‐ and macroscopic field variables, and a weak coupling solution method is employed to solve the two‐way coupling phenomena between the diffusion of scalar fields and the deformation of quasi‐brittle solids. The macroscopic mechanical behavior represented by the derived two‐scale two‐way coupled model reveals material nonlinearity due to micro‐scale cracking induced by the scalar‐field‐induced deformation, which can be simulated by the finite cover method. After verifying the fundamental validity of the proposed model and the analysis method, we perform a simple numerical example to demonstrate their ability to predict aging material deterioration. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

9.
    
In this paper, we prove that the Algebraic A‐FETI method corresponds to one particular instance of the original one‐level FETI method. We also report on performance comparisons on an Origin 2000 between the one‐ and two‐level FETI methods and an optimized sparse solver, for two industrial applications: the stress analysis of a thin shell structure, and that of a three‐dimensional structure modelled by solid elements. These comparisons suggest that for topologically two‐dimensional problems, sparse solvers are effective when the number of processors is relatively small. They also suggest that for three‐dimensional applications, scalable domain decomposition methods such as FETI deliver a superior performance on both sequential and parallel hardware configurations. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

10.
    
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.  相似文献   

11.
    
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.  相似文献   

12.
    
An extension of the FETI‐H method is designed for the solution of acoustic scattering problems with multiple right‐hand sides. A new local pre‐conditioning of this domain decomposition method is also presented. The potential of the resulting iterative solver is demonstrated by numerical experiments for two‐dimensional problems with high wavenumbers, as many as 2.5 million complex degrees of freedom, and a sweep on the angle of the incident wave. Preliminary results for a three‐dimensional submarine problem are also included. The FETI‐H method, whose numerical scalability with respect to the mesh and subdomain sizes was previously established, is shown here to be also numerically scalable with respect to the wavenumber. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

13.
    
A hybrid multiscale framework is presented, which processes the material scales in a concurrent manner, borrowing features from hierarchical multiscale methods. The framework is used for the analysis of non‐linear heterogeneous materials and is capable of tackling strain localization and failure phenomena. Domain decomposition techniques, such as the ?nite element tearing and interconnecting method, are used to partition the material in a number of non‐overlapping domains and adaptive re?nement is performed at those domains that are affected by damage processes. This re?nement is performed in terms of material scale and ?nite element size. It is veri?ed that the results are independent of the chosen domain decomposition. Moreover, the multiscale analyses are validated with reference solutions obtained with a full ?ne‐scale solution procedure. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

14.
    
We present a novel partitioned coupling algorithm to solve first‐order time‐dependent non‐linear problems (e.g. transient heat conduction). The spatial domain is partitioned into a set of totally disconnected subdomains. The continuity conditions at the interface are modeled using a dual Schur formulation where the Lagrange multipliers represent the interface fluxes (or the reaction forces) that are required to maintain the continuity conditions. The interface equations along with the subdomain equations lead to a system of differential algebraic equations (DAEs). For the resulting equations a numerical algorithm is developed, which includes choosing appropriate constraint stabilization techniques. The algorithm first solves for the interface Lagrange multipliers, which are subsequently used to advance the solution in the subdomains. The proposed coupling algorithm enables arbitrary numeric schemes to be coupled with different time steps (i.e. it allows subcycling) in each subdomain. This implies that existing software and numerical techniques can be used to solve each subdomain separately. The coupling algorithm can also be applied to multiple subdomains and is suitable for parallel computers. We present examples showing the feasibility of the proposed coupling algorithm. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

15.
    
An integrated framework and computational technology is described that addresses the issues to foster absolute scalability (A‐scalability) of the entire transient duration of the simulations of implicit non‐linear structural dynamics of large scale practical applications on a large number of parallel processors. Whereas the theoretical developments and parallel formulations were presented in Part 1, the implementation, validation and parallel performance assessments and results are presented here in Part 2 of the paper. Relatively simple numerical examples involving large deformation and elastic and elastoplastic non‐linear dynamic behaviour are first presented via the proposed framework for demonstrating the comparative accuracy of methods in comparison to available experimental results and/or results available in the literature. For practical geometrically complex meshes, the A‐scalability of non‐linear implicit dynamic computations is then illustrated by employing scalable optimal dissipative zero‐order displacement and velocity overshoot behaviour time operators which are a subset of the generalized framework in conjunction with numerically scalable spatial domain decomposition methods and scalable graph partitioning techniques. The constant run times of the entire simulation of ‘fixed‐memory‐use‐per‐processor’ scaling of complex finite element mesh geometries is demonstrated for large scale problems and large processor counts on at least 1024 processors. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

16.
This contribution presents a numerical strategy to evaluate the effective properties of image‐based microstructures in the case of random material properties. The method relies on three points: (1) a high‐order fictitious domain method; (2) an accurate spectral stochastic model; and (3) an efficient model‐reduction method based on the proper generalized decomposition in order to decrease the computational cost introduced by the stochastic model. A feedback procedure is proposed for an automatic estimation of the random effective properties with a given confidence. Numerical verifications highlight the convergence properties of the method for both deterministic and stochastic models. The method is finally applied to a real 3D bone microstructure where the empirical probability density function of the effective behaviour could be obtained. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

17.
    
A sequential multi‐scale homogenization method combined with molecular dynamics (MD) simulation is developed for the mechanical characterization of nanoparticulate composites. In order to characterize the particle‐size effect of nanocomposites, the effective interface, which has been adopted in continuum micromechanics approaches, is considered as the characteristic phase. Owing to the existence of the interface and the size‐dependent elastic modulus that is observed from MD simulations, an analysis of the mechanical properties of nanocomposites with continuum micromechanics requires careful consideration of the particle‐concentration effect. Therefore, this study focuses on hierarchical information transfer from the molecular model to the continuum model through the homogenization method in lieu of an analytical micromechanics bridging method. Using the present multi‐scale homogenization method, the elastic properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. In addition, the overall elastic modulus of nanocomposites is obtained from the present model and compared with the results of MD simulation, the micromechanics bridging model, and finite‐element analysis (FEA). Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

18.
    
This paper presents a strategy for the computation of structures with repeated patterns based on domain decomposition and block‐Krylov solvers. It can be seen as a special variant of the FETI method. We propose using the presence of repeated domains in the problem to compute the solution by minimizing the interface error on several directions simultaneously. The method not only drastically decreases the size of the problems to solve but also accelerates the convergence of interface problem for nearly no additional computational cost and minimizes expensive memory accesses. The numerical performances are illustrated on some thermal and elastic academic problems. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

19.
    
This work presents a partitioned finite element formulation for flexible multibody systems, based on the floating frame (FF) approach, under the assumption of small deformations but arbitrarily large rotations of the bodies. In classical FF of reference methods, deformational modes are normally computed by modal analysis. In this approach, free‐floating modes are eliminated from the linear model using projection techniques and substituted by a complete set of non‐linear finite rotations. In this way, all deformational modes are retained, and no modal selection is needed. The main difference between this work and a classical FF of reference formulation is an algebraic separation of pure deformational modes from rigid‐body motions. The proposed methodology presents the following advantages. First, the position and orientation of the FF has no restriction and can be freely located in the body with identical results. Second, the formulation uses only the linear finite element matrices of a classical vibration problem; hence, they can be easily obtained from linear FEM packages. Third, no selection of modes is needed, all deformational modes are retained through the filtering process. And finally, thanks to the use of localized Lagrangian multipliers (LLM), a partitioned system is obtained that can be solved iteratively and in a distributed manner by available scalable solvers. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

20.
    
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element and domain decomposition methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a domain decomposition iterative solver) from the discretization error (due to the finite element), which enables the steering of the iterative solver by the discretization error. These lower bounds are also used to improve the goal‐oriented error estimation in a substructured context. Assessments on 2D static linear mechanic problems illustrate the relevance of the separation of sources of error and the lower bounds' independence from the substructuring. We also steer the iterative solver by an objective of precision on a quantity of interest. This strategy consists in a sequence of solvings and takes advantage of adaptive remeshing and recycling of search directions. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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