Non-overlapping domain decomposition methods in structural mechanics

Gosselet, Pierre; Rey, Christian

doi:10.1007/bf02905857

Cited by 135 publications

(165 citation statements)

References 75 publications

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“…Furthermore, it has to be noted that the non-intrusive local enrichment of NURBS patches may not be the only application of such a method. Indeed, taking advantage of the Lagrange multipliers approach, the proposed methodology seems to be adapted to the development of more regular non-overlapping domain decomposition methods to be used for high performance computing on parallel computer architectures (see, e.g., [42][43][44] for the elaboration in the context of classical FEM). In addition, in the same idea of what is performed in [52], such a coupling may also serve as a basis to develop a strategy that could connect different NURBS patches while ensuring a C 1 continuity at the interface.…”

Section: Resultsmentioning

confidence: 99%

“…Indeed, the communication between the subdomains is performed via the Lagrange multiplier only. This feature is the basis of the non-overlapping domain decomposition methods developed for high performance computing on parallel computer architectures (see, e.g., [42][43][44]). In the same idea, such a property enables to build non-intrusive coupling algorithms for the modeling of local behaviors (see, e.g., [14,12,32,[34][35][36]).…”

Section: A Review Of the Classical Mortar Approachmentioning

confidence: 99%

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Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Bouclier

Passieux

Salaün

2017

Computer Methods in Applied Mechanics and Engineering

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of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches. (2017) Highlights• We develop a new mortar method for NURBS that keeps the benefit of using more regular functions.• We propose to match the tractions in addition to the displacements at the coupling interface.• We apply the methodology to perform the non-intrusive local enrichment of NURBS patches.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we develop a mortar method for the coupling of non-conforming NURBS subdomains within a NURBS patch that keeps the benefit of using more regular functions. The idea is to use two Lagrange multipliers to match, across the coupling interface, the tractions coming from the discrete displacements in addition to the discrete displacements. It results in a strategy that is suitable with the continuity of the physical solution: when the physical solution is sufficiently smooth, the strategy enables to represent a C 1 behavior; but, when only a C 0 displacement is expected, no additional errors are introduced since only the traction force is continuous and not the whole derivative fields. Lower stress jumps at the coupling interface can then be observed which allows for a better transition of the information. As an application, a non-intrusive algorithm is also built to solve the proposed coupling method, which enables simple and flexible local enrichments of NURBS patches without losing the interest of using more regular functions. A range of numerical examples in two-dimensional linear elasticity are carried out along with comparisons with other published NURBS coupling techniques to demonstrate the performance of the proposed coupling and its interest when combined to a non-intrusive strategy.

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Section: Resultsmentioning

confidence: 99%

Section: A Review Of the Classical Mortar Approachmentioning

confidence: 99%

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Bouclier

Passieux

Salaün

2017

Computer Methods in Applied Mechanics and Engineering

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“…FETI-1 [13,14,12,23] is a non-overlapping DDM [16]. Thus, it is based on decomposing the original spatial domain into non-overlapping subdomains.…”

Section: Permonfllopmentioning

confidence: 99%

“…The first option is to use a numerical approach [16], and the second one is to generate R as rigid body modes from the mesh nodal coordinates [22]. The latter is typical for TFETI and is considered here.…”

Section: Permonfllopmentioning

confidence: 99%

Solving Contact Mechanics Problems with PERMON

Hapla

Horák

Pospíšil

et al. 2016

Lecture Notes in Computer Science

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Abstract. PERMON makes use of theoretical results in quadratic programming algorithms and domain decomposition methods. It is built on top of the PETSc framework for numerical computations. This paper describes its fundamental packages and shows their applications. We focus here on contact problems of mechanics decomposed by means of a FETI-type nonoverlapping domain decomposition method. These problems lead to inequality constrained quadratic programming problems that can be solved by our PermonQP package.

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“…In the context of such huge calculations, multiscale approaches based on domain decomposition methods [1] or on model superposition [2,3] are widely used. Another popular family of strategies is based on computational homogenization, i.e.…”

Section: Introductionmentioning

confidence: 99%

A PGD-based homogenization technique for the resolution of nonlinear multiscale problems

Cremonesi

Néron

Guidault

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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This paper deals with the offline resolution of nonlinear multiscale problems leading to a PGD-reduced model from which one can derive microinformation which is suitable for design. Here, we focus on an improvement to the Proper Generalized Decomposition (PGD) technique which is used for the calculation of the homogenized operator and which plays a central role in our multiscale computational strategy. This homogenized behavior is calculated offline using the LATIN multiscale strategy, and PGD leads to a drastic reduction in CPU cost. Indeed, the multiscale aspect of the LATIN method is based on splitting the unknowns between a macroscale and a microcomplement. This macroscale is used to capture the homogenized behavior of the structure and then to accelerate the convergence of the iterative algorithm. The novelty of this work lies in the reduction of the computation cost of building the homogenized operator. In order to do that, the problems defined within each subdomain are solved using a new PGD representation of the unknowns in which the separation of the unknowns is performed not only in time and in space, but also in terms of the interface macrodisplacements. The numerical example presented shows that the convergence rate of the approach is not affected by this new representation and that a significant reduction in computation cost can be achieved, particularly in the case of nonlinear behavior. The technique used herein is then particularly important to enhance the performances of the LATIN strategy but is not limited to this method. The more general path which is followed in this paper is to solve the microproblems arising in the homogenization for all the configurations that can be encountered in the calculation. An additional and novel benefit of this approach is that it includes the calculation of the homogenized tangent operator which gives, over the whole time interval and for any cell, the relation between the perturbation in terms of macroforces and the perturbation in terms of macrodisplacements. In linear viscoelasticity, this operator represents the homogenized behavior of the structure exactly

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Non-overlapping domain decomposition methods in structural mechanics

Cited by 135 publications

References 75 publications

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Solving Contact Mechanics Problems with PERMON

A PGD-based homogenization technique for the resolution of nonlinear multiscale problems

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