A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers

Bosy, Michał; Montardini, Monica; Sangalli, Giancarlo; Tani, Mattia

doi:10.1016/j.camwa.2020.08.024

Cited by 11 publications

(12 citation statements)

References 30 publications

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“…In this sense, our method is consistent with the current development of open-source IG libraries (see, e.g., Nutils (http://www.nutils.org) or pyiga (https://github.com/c-f-h/pyiga) as Python libraries, tIGAr [40] for a FENICS-based implementation, and YETI (https://lamcosplm.insa-lyon.fr/projects/yeti/) for a Fortran-Python implementation). Even more interestingly, since the IG code is only used at the global scale, where standard elasticity may be sufficient, our strategy also appears totally relevant with the newly developed fast assembly and solution procedures for IGA in the linear regime (see, e.g., sum factorization [58], use of look-up tables [59,60], weighted quadrature [61], and domain decomposition solvers [62,63]).…”

Section: Discussionmentioning

confidence: 99%

A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena

et al. 2022

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This work undertakes to combine the interests of IsoGeometric Analysis (IGA) and standard Finite Element Methods (FEM) for the global/local simulation of structures. The idea is to adopt a hybrid global-IGA/local-FEM modeling, thereby benefiting from: (i) the superior geometric description and per-Degree-Of-Freedom accuracy of IGA for capturing global, regular responses, and (ii) the ability of FEM to compute local, strongly non-linear or even singular behaviors. For the sake of minimizing the implementation effort, we develop a coupling scheme that is fully non-invasive in the sense that the initial global spline model to be enriched is never modified and the construction of the coupling operators can be performed using conventional FE packages. The key ingredient is to express the FEM-to-IGA bridge, based on Bézier extraction, to transform the initial global spline interface into a FE one on which the local FE mesh can be constructed. This allows to resort to classic FE trace operators to implement the coupling. It results in a strategy that offers the opportunity to simply couple an isogeometric code with any robust FE code suitable for the modelling of complex local behaviors. The method also easily extends in case the users only have at their disposal FE codes. This is the situation that is considered for the numerical illustrations. More precisely, we only make use of the FE industrial software Code Aster to perform efficiently and accurately the hybrid global-IGA/local-FEM simulation of structures subjected locally to cracks, contact, friction and delamination.

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Section: Discussionmentioning

confidence: 99%

A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena

et al. 2022

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“…For that purpose, the use of Domain-Decomposition Methods appears to us very attractive, see for example [12,34]. In order to push the multiscale philosophy during the resolution too, one may apply multiscale DDMs [28,44,68].…”

Section: Toward a Matrix-free Approachmentioning

confidence: 99%

“…For this matrix-free approach to be valid, the preconditioning step needs to follow the same philosophy. For that purpose, the use of Domain-Decomposition Methods appears to us very attractive, see for example [ 12 , 34 ]. In order to push the multiscale philosophy during the resolution too, one may apply multiscale DDMs [ 28 , 44 , 68 ].…”

Section: Extension To Other Quantities Of Interestmentioning

confidence: 99%

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Fast and multiscale formation of isogeometric matrices of microstructured geometric models

2021

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The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly time in the context of isogeometric linear elasticity of complex microstructured geometries modeled via spline compositions. The developed isogeometric approach involves a polynomial approximation occurring at the macro-scale and the use of lookup tables with pre-computed integrals incorporating the micro-scale information. We provide theoretical insights and numerical examples to investigate the performance of the procedure. The strategy turns out to be of great interest not only to form finite element operators but also to compute other quantities in a fast manner as for instance sensitivity analyses commonly used in design optimization.

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“…The idea of FETI has already been adapted to IgA, cf. [16,12,23,3], and is sometimes called Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method.…”

Section: Introductionmentioning

confidence: 99%

A IETI-DP method for discontinuous Galerkin discretizations in Isogeometric Analysis with inexact local solvers

Montardini¹,

Sangalli²,

Schneckenleitner³

et al. 2022

Preprint

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We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows the consideration of discretizations that do not match on the interfaces. We solve the resulting linear system using a Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method. We are interested in solving the arising patch-local problems using iterative solvers since this allows the reduction of the memory footprint. We solve the patchlocal problems approximately using the Fast Diagonalization method, which is known to be robust in the grid size and the spline degree. To obtain the tensor structure needed for the application of the Fast Diagonalization method, we introduce an orthogonal splitting of the local function spaces. We present a convergence theory that confirms that the condition number of the preconditioned system only grows polylogarithmically with the grid size. The numerical experiments confirm this finding. Moreover, they show that the convergence of the overall solver only mildly depends on the spline degree. We observe a mild reduction of the computational times and a significant reduction of the memory requirements in comparison to standard IETI-DP solvers using sparse direct solvers for the local subproblems. Furthermore, the experiments indicate good scaling behavior on distributed memory machines.

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A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers

Cited by 11 publications

References 30 publications

A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena

A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena

Fast and multiscale formation of isogeometric matrices of microstructured geometric models

A IETI-DP method for discontinuous Galerkin discretizations in Isogeometric Analysis with inexact local solvers

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