A Nonlinear Dual-Domain Decomposition Method: Application to Structural Problems with Damage

Pebrel, Julien; Rey, Christian; Gosselet, Pierre

doi:10.1615/intjmultcompeng.v6.i3.50

Cited by 48 publications

(53 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For problems with high nonlinearities, preconditioning techniques on the nonlinear level, such as the additive Schwarz preconditioned inexact Newton (ASPIN) methods [9,25,39], the nonlinear restricted Schwarz preconditioners [10,16], the nonlinear dual-domain decomposition methods [48], the nonlinear balancing domain decomposition by constraints methods [30], the nonlinear elimination methods [26,27,29], and the composite nonlinear algebraic methods [6], have received increasing attention in recent years. In particular, some efforts have been made in applying the ASPIN method to solve the two-phase flow problems [51,53].…”

Section: B595mentioning

confidence: 99%

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

Yang¹,

Yang²,

Sun³

2016

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

show abstract

Section: B595mentioning

confidence: 99%

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

Yang¹,

Yang²,

Sun³

2016

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…can refer for instance to expressions (11) or (12), F is a small-sized m × m square matrix, and V an interface vectors basis of size n A ×m. Writing…”

Section: Spring In Series Modelmentioning

confidence: 99%

“…This article focuses on the nonlinear substructuring and condensation method, which has been investigated in previous studies [10,11,12,13]. The substructured formulation involves a choice of interface transmission conditions, which can be either primal, dual or mixed, referring either to interface displacements, nodal interface reactions, or a linear combination of the two previous types -i.e.…”

Section: Introductionmentioning

confidence: 99%

Substructured formulations of nonlinear structure problems - influence of the interface condition

Negrello

Gosselet

Rey

et al. 2016

Int. J. Numer. Meth. Engng

Self Cite

View full text Add to dashboard Cite

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM 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 usally 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.

show abstract

“…This formulation is very similar to nonlinear domain decomposition methods [8]. The difference is that the global model is never substructured since the approach is non-intrusive; therefore, the complement area is never separated from the area of interest in the global model, and the quantities S G ,C and b G ,C cannot be accessed directly.…”

Section: Interface Formulationmentioning

confidence: 99%

A two‐scale approximation of the Schur complement and its use for non‐intrusive coupling

Gendre

Allix

Gosselet

2011

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYThis paper presents a two-scale approximation of the Schur complement of a subdomain's stiffness matrix, obtained by combining local (i.e. element strips) and global (i.e. homogenized) contributions. This approximation is used in the context of a coupling strategy that is designed to embed local plasticity and geometric details into a small region of a large linear elastic structure; the strategy consists in creating a local model that contains the desired features of the concerned region and then substituting it into the global problem by the means of a non-intrusive solver coupling technique adapted from domain decomposition methods. Using the two-scale approximation of the Schur complement as a Robin condition on the local model enables to reach high efficiency. Examples include a large 3D problem provided by our industrial partner Snecma.

show abstract

A Nonlinear Dual-Domain Decomposition Method: Application to Structural Problems with Damage

Cited by 48 publications

References 15 publications

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

Substructured formulations of nonlinear structure problems - influence of the interface condition

A two‐scale approximation of the Schur complement and its use for non‐intrusive coupling

Contact Info

Product

Resources

About