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1.
Camille Negrello Pierre Gosselet Christian Rey 《International journal for numerical methods in engineering》2018,114(7):675-693
An efficient method for solving large nonlinear problems combines Newton solvers and domain decomposition methods. In the domain decomposition method framework, the boundary conditions can be chosen to be primal, dual, or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance), which can increase the convergence rate. The optimal value for this parameter is usually too expensive to be computed exactly in practice: An approximate version has to be sought, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance, which combines short‐ and long‐range effects at a low computational cost. 相似文献
2.
Charbel Farhat Po-Shu Chen Jan Mandel 《International journal for numerical methods in engineering》1995,38(22):3831-3853
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. 相似文献
3.
P. Kerfriden J. C. Passieux S. P. A. Bordas 《International journal for numerical methods in engineering》2012,89(2):154-179
This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and propagation while concentrating the computational effort where it is most needed, that is, in the localization zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe damage and cracking) is solved for in a reduced space computed by the classical proper orthogonal decomposition while the local (master) degrees of freedom (associated with the part of the structure where most of the damage is taking place) are fully resolved. Both domains are coupled through a local/global technique. This method circumvents the difficulties associated with model order reduction for the simulation of highly nonlinear mechanical failure and offers an alternative or complementary approach to the development of multiscale fracture simulators. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
4.
Daniel J. Rixen Charbel Farhat Radek Tezaur Jan Mandel 《International journal for numerical methods in engineering》1999,46(4):501-533
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
5.
Charbel Farhat Marion Chandesris 《International journal for numerical methods in engineering》2003,58(9):1397-1434
A methodology for squeezing the most out of massively parallel processors when solving partial differential evolution equations by implicit schemes is presented. Its key components include a preferred implicit time‐integrator, a decomposition of the time‐domain into time‐slices, independent time‐integrations in each time‐slice of the semi‐discrete equations, and Newton‐type iterations on a coarse time‐grid. Hence, this methodology parallelizes the time‐loop of a time‐dependent partial differential equation solver without interfering with its sequential or parallel space‐computations. It is particularly interesting for time‐dependent problems with a few degrees of freedom such as those arising in robotics and protein folding applications, where the opportunities for parallelization over the degrees of freedom are limited. Error and stability analyses of the proposed parallel methodology are performed for first‐ and second‐order hyperbolic problems. Its feasibility and impact on reducing the solution time below what is attainable by methods which address only parallelism in the space‐domain are highlighted for fluid, structure, and coupled fluid–structure model problems. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
6.
F. J. Lingen M. G. A. Tijssens 《International journal for numerical methods in engineering》2001,52(8):867-888
Simulations of crack growth that are based on the cohesive surface methodology typically involve ill‐conditioned systems of equations and require much processing time. This paper shows how these systems of equations can be solved efficiently by adopting the domain decomposition approach in which the finite element mesh is partitioned into multiple blocks. The system of equations is then reduced to a much smaller system of equations that is solved with an iterative algorithm in combination with a powerful two‐level preconditioner. Although the solution algorithm is more efficient than a direct solution algorithm on a single‐processor computer, it becomes really attractive when used on a parallel computer. This is demonstrated for a large scale simulation of crack growth in a polymer using a Cray T3E with 64 processors. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
7.
The work reported in this paper is motivated by the need to develop portable parallel processing algorithms and codes which
can run on a variety of hardware platforms without any modifications. The prime aim of the research work reported here is
to test the portability of the parallel algorithms and also to study and understand the comparative efficiencies of three
parallel algorithms developed for implicit time integration technique. The standard message passing interface (MPI) is used
to develop parallel algorithms for computing nonlinear dynamic response of large structures employing implicit time-marching
scheme. The parallel algorithms presented in this paper are developed under the broad framework of non-overlapped domain decomposition
technique. Numerical studies indicate that the parallel algorithm devised employing the conventional form of Newmark time
integration algorithm is faster than the predictor-corrector form. It is also accurate and highly adaptive to fine grain computations.
The group implicit algorithm is found to be extremely superior in performance when compared to the other two parallel algorithms.
This algorithm is better suited for large size problems on coarse grain environment as the resulting submeshes will obviously
be large and thus permit larger time steps without losing accuracy. 相似文献
8.
Parallel computation of a damage localization problem using parallel multifrontal solver 总被引：1，自引：0，他引：1
In this paper, nonlinear parallel structural analyses are performed using a distributed memory sparse direct multifrontal linear solver. The linear solver is fully parallel, working with substructures determined by a parallel graph partitioner. The parallel performance of the nonlinear parallel algorithm is demonstrated using damage localization problems for two and three dimensional crack models. Convergence studies of the predicted local variation of damage at the crack tip are performed using discretizations with up to one million degrees of freedom. Implementation issues for damage localization problems are discussed, including the selection of independent variables and the use of Riks continuation method.We acknowledge the financial support of Ministry of Science and Technology by National Research Laboratory program. (grant number 00-N-NL-01-C-026) 相似文献
9.
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. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
10.
Pierre Gosselet Daniel Rixen François‐Xavier Roux Nicole Spillane 《International journal for numerical methods in engineering》2015,104(10):905-927
Domain decomposition methods often exhibit very poor performance when applied to engineering problems with large heterogeneities. In particular, for heterogeneities along domain interfaces, the iterative techniques to solve the interface problem are lacking an efficient preconditioner. Recently, a robust approach, named finite element tearing and interconnection (FETI)–generalized eigenvalues in the overlaps (Geneo), was proposed where troublesome modes are precomputed and deflated from the interface problem. The cost of the FETI–Geneo is, however, high. We propose in this paper techniques that share similar ideas with FETI–Geneo but where no preprocessing is needed and that can be easily and efficiently implemented as an alternative to standard domain decomposition methods. In the block iterative approaches presented in this paper, the search space at every iteration on the interface problem contains as many directions as there are domains in the decomposition. Those search directions originate either from the domain‐wise preconditioner (in the simultaneous FETI method) or from the block structure of the right‐hand side of the interface problem (block FETI). We show on two‐dimensional structural examples that both methods are robust and provide good convergence in the presence of high heterogeneities, even when the interface is jagged or when the domains have a bad aspect ratio. The simultaneous FETI was also efficiently implemented in an optimized parallel code and exhibited excellent performance compared with the regular FETI method. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
Radek Tezaur Antonini Macedo Charbel Farhat 《International journal for numerical methods in engineering》2001,51(10):1175-1193
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
12.
D. R. OAKLEY N. F. KNIGHT 《International journal for numerical methods in engineering》1996,39(2):235-259
A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for non-linear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly non-linear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly non-linear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the non-linear static response of two- and three-dimensional hyperelastic systems involving contact. Impressive relative speed-ups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing. 相似文献
13.
J. E. P. Monteagudo A. Firoozabadi 《International journal for numerical methods in engineering》2007,69(4):698-728
In this work, we compare the fully implicit (FI) and implicit pressure‐explicit saturation (IMPES) formulations for the simulation of water injection in fractured media. The system of partial differential equations is discretized within the discrete‐fracture framework using a control‐volume method. A unique feature of the methodology is that there is no need for the computation of matrix–fracture transfer terms. The non‐linear system of equations resulting from the FI formulation is solved with state‐of‐the‐art Newton and tensor methods. Direct and Krylov iterative methods are employed to solve the system resulting from the Newton linearization. The performance of the FI and IMPES formulations is compared with numerical testing. Results show that the contrast between matrix and fracture properties affects the performance of both IMPES and FI formulations and that the tensor method outperforms all the Newton solvers for the near‐singular Jacobian matrix. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
X. Antoine A. Bendali M. Darbas 《International journal for numerical methods in engineering》2004,61(8):1310-1331
Since the advent of the fast multipole method, large‐scale electromagnetic scattering problems based on the electric field integral equation (EFIE) formulation are generally solved by a Krylov iterative solver. A well‐known fact is that the dense complex non‐hermitian linear system associated to the EFIE becomes ill‐conditioned especially in the high‐frequency regime. As a consequence, this slows down the convergence rate of Krylov subspace iterative solvers. In this work, a new analytic preconditioner based on the combination of a finite element method with a local absorbing boundary condition is proposed to improve the convergence of the iterative solver for an open boundary. Some numerical tests precise the behaviour of the new preconditioner. Moreover, comparisons are performed with the analytic preconditioner based on the Calderòn's relations for integral equations for several kinds of scatterers. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
The hydrodynamic interactions in a suspension of small particles in a viscous fluid is computed by a boundary integral velocity representation featuring a completed double-layer potential (completed double-layer boundary integral equation method or CDL = BIEM). A multiple expansion is used to represent interactions between distance particles, leading to a considerable improvement in computational speed. The resulting large linear system of equations provides an ideal setting for asynchronous iterative solvers (block Gauss-Seidel) on a message-passing MIMD parallel computer (Intel iPSC/860 Hypercube) using a supervisor-workers load-balancing strategy. Our benchmark results as a function of problem size and number of processors suggest that our algorithm will scale successfully to the massively parallel computers of the future. 相似文献
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Rongliang Chen Xiao‐Chuan Cai 《International journal for numerical methods in engineering》2014,99(13):945-965
A two‐level domain decomposition method is introduced for general shape optimization problems constrained by the incompressible Navier–Stokes equations. The optimization problem is first discretized with a finite element method on an unstructured moving mesh that is implicitly defined without assuming that the computational domain is known and then solved by some one‐shot Lagrange–Newton–Krylov–Schwarz algorithms. In this approach, the shape of the domain, its corresponding finite element mesh, the flow fields and their corresponding Lagrange multipliers are all obtained computationally in a single solve of a nonlinear system of equations. Highly scalable parallel algorithms are absolutely necessary to solve such an expensive system. The one‐level domain decomposition method works reasonably well when the number of processors is not large. Aiming for machines with a large number of processors and robust nonlinear convergence, we introduce a two‐level inexact Newton method with a hybrid two‐level overlapping Schwarz preconditioner. As applications, we consider the shape optimization of a cannula problem and an artery bypass problem in 2D. Numerical experiments show that our algorithm performs well on a supercomputer with over 1000 processors for problems with millions of unknowns. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
P.‐A. Boucard D. Odièvre F. Gatuingt 《International journal for numerical methods in engineering》2011,88(7):657-672
The objective of this work is to develop an efficient strategy for the parametric study of dynamic problems involving contacts with friction. Our approach is based on the multiscale LATIN method with domain decomposition. This is a mixed method that deals with the forces and velocities at the interfaces between the different subdomains simultaneously. We propose to take advantage of the capability of the multiscale LATIN method, called the multiparametric strategy, to reuse the solution of a given problem in order to solve similar problems. This strategy has already been applied successfully to a variety of static problems; here, it is extended to dynamics. First, we present the multiscale strategy in dynamics. Then, we show how the multiparametric strategy can be extended to dynamics. We illustrate the capabilities of the method through an academic 3D example and the simulation of a bolted joint. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
20.
本文给出了一阶迎风差分、内边界二阶迎风差分和二阶迎风差分三种格式的算法和误差估计。为了减弱稳定性条件限制,先在内边界点上采用小时间步长和大的空间步长进行多层计算,再在内点用隐格式并行计算。这些算法结合了迎风和区域分解的优点,计算格式简单,易于编程实现。 相似文献