A Numerically Scalable Domain Decomposition Method For The Solution Of Frictionless Contact Problems

this paper is to present an alternative domain decomposition method for the solution of frictionless contact problems that is also based on the FETI method, and which for this reason is named the FETI-C method (as in FETI-Contact). FETI-C is in many aspects different from the domain decomposition method recently proposed in [11] for solving frictionless contact problems. Indeed, the solution strategy described in [11] is organized around two levels of iterations, the first one aimed at satisfying the contact conditions, and the second one at satisfying, among other things, the equilibrium conditions. In the outer-iterations, an active zone of contact is updated by a mathematical programming technique. In the inner-iterations, a minimal subregion of the previously predicted area of contact is frozen and a state of equilibrium is sought after. In the FETI-C method described in this paper, both contact and equilibrium conditions are updated by a single iterative procedure. Most importantly, the FETI-C method incorporates an auxiliary "coarse contact problem" which not only guides the prediction of the active zone of contact, but also appears to ensure the numerical scalability of the proposed solution method with respect to both the number of subdomains, and the size of the problem. These numerical scalability properties are demonstrated numerically in this paper. For simplicity, and without any loss of generality, we consider here only the case where the subdomains in contact have matching discrete interfaces. We also assume that all structural components undergo small deformations as well as small displacements and rotations. In Section 2, we review the FETI method in order to keep this paper as self-contained as possible. In Section 3, we overview the formulation of the..

A time multi-time-scale strategy for multiphysics problems:application to poroelasticity

Usually, multiphysics phenomena and coupled-field problems lead to computationally intensive structural analysis. Strategies to keep these problems computationally affordable are of special interest. For coupled fluid-structure problems, for instance, partitioned procedures and staggered algorithms are often preferable to direct analysis. In a previous article, a new strategy derived from the LArge Time INcrement (LATIN) method was described. This strategy was applied to the consolidation of saturated porous soils, which is a highly coupled fluid-solid problem. The feasibility of the method and the comparison of its performance with that of a standard partitioning scheme (the so-called ISPP method) was presented. Here, we go one step further and use the LATIN method to take into account the different time scales that usually arise from the different physics. We propose a multi-time-scale strategy, which improves the existing method

An extension of the FETI domain decomposition method for incompressible and nearly incompressible problems

Incompressible and nearly incompressible problems are treated herein with a mixed finite element formulation in order to avoid ill-conditioning that prevents accuracy in pressure estimation and lack of convergence for iterative solution algorithms. A multilevel dual domain decomposition method is then chosen as an iterative algorithm: the original FETI and FETI-DP methods are extended to deal with such problems, when the discretization of the pressure field is discontinuous throughout the elements. A dedicated augmentation of the algorithms is proposed and the di#erent methods are compared with several preconditioners, for bidimensional test cases. The resulting approaches are both optimal and numerically scalable, and their costs are estimated with a complexity analysis

A Micro-Macro And Parallel Computational Strategy For Highly-Heterogeneous Structures

this paper. For a perfect interface, contains the transmission conditions for forces: Y Q Q@Y Q and for displacements: ('^ QXQZY \u7f V o V Q !" $ s jBj Y 5 + (U^ QXQZY ! \u7f V Q o Q@Y !" + s jBj Y also contains the boundary conditions for boundary interfaces included in o

A Computational Strategy For Multiphysics Problems - Application To Poroelasticity

this paper, we describe a new strategy for solving coupled multiphysics problems which is built upon the LArge Time INcrement (LATIN) method. The proposed application concerns the consolidation of saturated porous soil, which is a strongly coupled fluid-solid problem. The goal of this paper is to discuss the efficiency of the proposed approach, especially when using an appropriate time-space approximation of the unknowns for the iterative resolution of the uncoupled global problem. The use of a set of radial loads as an adaptive approximation of the solution during iteration will be validated and a strategy for limiting the number of global resolutions will be tested on multiphysics problems. Copyright c 2000 John Wiley & Sons, Lt

A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff–Love shells

International audienceOriginally, Isogeometric Analysis aimed at using geometric models for the structural analysis. The actual realization of this objective to complex real-world structures requires a special treatment of the non-conformities between the patches generated during the geometric modeling. Different advanced numerical tools now enable to analyze elaborated multipatch models, especially regarding the imposition of the interface coupling conditions. However, in order to push forward the isogeometric concept, a closer look at the algorithm of resolution for multipatch geometries seems crucial. Hence, we present a dual Domain Decomposition algorithm for accurately analyzing non-conforming multi-patch Kirchhoff-Love shells. The starting point is the use of a Mortar method for imposing the coupling conditions between the shells. The additional degrees of freedom coming from the Lagrange multiplier field enable to formulate an interface problem, known as the one-level FETI problem. The interface problem is solved using an iterative solver where, at each iteration, only local quantities defined at the patch level (i.e. per sub-domain) are involved which makes the overall algorithm naturally parallelizable. We study the preconditioning step in order to get an algorithm which is numerically scalable. Several examples ranging from simple benchmark cases to semi-industrial problems highlight the great potential of the method

Folding a better checkerboard

Folding an n ×n checkerboard pattern from a square of paper that is white on one side and black on the other has been thought for several years to require a paper square of semiperimeter n 2 [superscript 2]. Indeed, within a restricted class of foldings that match all previous origami models of this flavor, one can prove a lower bound of n 2 [superscript 2](though a matching upper bound was not known). We show how to break through this barrier and fold an n ×n checkerboard from a paper square of semiperimeter 1/2 n2 [superscript 2] + O(n) In particular, our construction strictly beats semiperimeter n 2 [superscript 2] for (even) n > 16, and for n = 8, we improve on the best seamless folding.National Science Foundation (U.S.) (CAREER award CCF-0347776