INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Deparis, Simone; Forti, Davide; Gervasio, Paola; Quarteroni, Alfio

doi:10.1016/j.compfluid.2016.03.033

Cited by 29 publications

(43 citation statements)

References 38 publications

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“…Overall, in terms of accuracy of the stress field, we can note that the corrected WACA approach allows to achieve, on average, a low error on the stresses and a low dispersion from case to case, as well as less extreme outliers, making it a pertinent alternative to the WRM/Mortar approach, while involving a lower implementation complexity and computational cost. Several other additional conclusions can be drawn based on the detailed study of the dependence of the error measures with mesh density (see figures [26][27][28][29]. In configuration (1)(figure 26) we can make following observations:…”

Section: Test Cases Definition and Analysis For Consistent Meshesmentioning

confidence: 74%

“…Here we describe the internodes approach, introduced for the first time by Deparis et al in [26] and further analyzed by Gervasio et al in [42]. We derived it's matrix formulation directly from equation (8).…”

Section: The Internodes Approachmentioning

confidence: 99%

“…The main difficulty of this approach consists in the choice of the penalty factor. Deparis et al introduced in [26] a new approach based on the simultaneous continuity of the displacement and the internal loads per unit of area at the interface. This promising techniques has been tested in the case of a simple patch test and more complex fluid structure interaction problems.…”

mentioning

confidence: 99%

“…In subsection 3.2 the variational principle and the Mortar formulation with Lagrange multipliers are summarized. The internodes [26] formulation is presented in subsection 3.3, starting from the physical hypothesis behind this method giving its matrix formulation. The simplicity of the internodes formulation inspired us to develop a new approach we call Weighted Average Continuity Approach (WACA), which seeks to maintain low implementation complexity and computational cost, similar to the Internodes apporach, but achieve improved stress accuracy, similar to the Mortar approach.…”

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confidence: 99%

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Weighted Average Continuity Approach and Moment Correction: New Strategies for Non-consistent Mesh Projection in Structural Mechanics

Coniglio

Gogu

Morlier

2018

Arch Computat Methods Eng

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Tying non-matching meshes is needed in many instances of finite element modeling. Multiple techniques have been proposed in the literature to accomplish the correct communication between different discretizations. They all seek to achieve some trade-off in terms of accuracy, complexity and computational cost. In this work we review several of the existing techniques and benchmark them on several simple test problems in terms of accuracy and computational cost. We also discuss some of the drawbacks and limitations of the existing methods. We then propose two novel contributions. First, a new approach that imposes the continuity of the displacement field at the interface in a point-wise manner only after an integral weighted averaging procedure over each interface. Second, a procedure for the correction of the interpolation operator based on the balance of internal forces and moments at the interface is proposed, which is applicable to all the reviewed methods, both existing and the new proposed one. All the considered approaches are benchmarked on several test problems in terms of various error measures for displacements, stresses, interface forces and moments, total work at the interface and computational cost.

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Section: Test Cases Definition and Analysis For Consistent Meshesmentioning

confidence: 74%

Section: The Internodes Approachmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Weighted Average Continuity Approach and Moment Correction: New Strategies for Non-consistent Mesh Projection in Structural Mechanics

Coniglio

Gogu

Morlier

2018

Arch Computat Methods Eng

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“…The implementation of the mortar method is not straightforward, as the algorithm is based on L 2 -projections of the traces of functional spaces defined on a group subdomains -the masters -onto the interfaces of the adjacent ones -the slaves. INTERNODES [15,16], a recently developed method for the treatment of non-conforming meshes, overcomes this issue by treating the transmission conditions with the interpolation of basis functions of the master domains onto the interfaces of the slaves.…”

Section: Introductionmentioning

confidence: 99%

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

Deparis

Pegolotti

2019

ESAIM: M2AN

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This work focuses on the development of a non-conforming domain decomposition method for the approximation of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a discrete number of Lagrange multipliers defined over the interfaces of adjacent subdomains. The method falls into the class of primal hybrid methods, which also include the well-known mortar method. Differently from the mortar method, we discretize the space of basis functions on the interface by spectral approximation independently of the discretization of the two adjacent domains; one of the possible choices is to approximate the interface variational space by Fourier basis functions. As we show in the numerical simulations, our approach is well-suited for the solution of problems with non-conforming meshes or with finite element basis functions with different polynomial degrees in each subdomain. Another application of the method that still needs to be investigated is the coupling of solutions obtained from otherwise incompatible methods, such as the finite element method, the spectral element method or isogeometric analysis.

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Parallel block‐preconditioned monolithic solvers for fluid‐structure interaction problems

Jodlbauer

Langer

Wick

2018

Numerical Meth Engineering

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In this work, we consider the solution of fluid-structure interaction (FSI) problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian-Eulerian framework and a nonlinear harmonic mesh motion model. Monolithic approaches require the solution of large ill-conditioned linear systems of algebraic equations at every Newton step. Direct solvers tend to use too much memory even for a relatively small number of degrees of freedom and, in addition, exhibit superlinear growth in arithmetic complexity. Thus, iterative solvers are the only viable option. To ensure convergence of iterative methods within a reasonable amount of iterations, good and, at the same time, cheap preconditioners have to be developed. We study physics-based block preconditioners, which are derived from the block-LDU factorization of the FSI Jacobian, and their performance on distributed memory parallel computers in terms of two-and three-dimensional test cases permitting large deformations. KEYWORDS fluid-structure interaction, monolithic formulation, parallel solvers, physics-based block preconditioners Int J Numer Methods Eng. 2019;117:623-643.wileyonlinelibrary.com/journal/nme

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INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Cited by 29 publications

References 38 publications

Weighted Average Continuity Approach and Moment Correction: New Strategies for Non-consistent Mesh Projection in Structural Mechanics

Weighted Average Continuity Approach and Moment Correction: New Strategies for Non-consistent Mesh Projection in Structural Mechanics

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

Parallel block‐preconditioned monolithic solvers for fluid‐structure interaction problems

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