Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations

Gervasio, Paola; Quarteroni, Alfio

doi:10.1016/j.cma.2018.02.004

Cited by 15 publications

(38 citation statements)

References 19 publications

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“…On the other hand the formulation and the implementation are straightforward if compared with the mortar and the WRM approaches: the only mass matrices M 2 , M 1 and the interolation operators Π 12 and Π 21 are needed. Good convergence property have been showed in the work of Gervasio et al [42].…”

Section: The Internodes Approachmentioning

confidence: 79%

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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: The Internodes Approachmentioning

confidence: 79%

“…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%

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 INTERNODES method has been analyzed in [21] in the Finite Element framework. More precisely, if quasi-uniform and affine triangulations are considered inside each subdomain and Lagrange interpolation is applied to enforce the interface conditions, it has been proved ( [21]) that INTERNODES yields a solution that is unique, stable, and convergent with an optimal rate of convergence (i.e., that of the best approximation error in every subdomain). Two interpolation operators are needed to guarantee the optimal convergence rate of the method with respect to the discretization parameters.…”

Section: Remark 32 (Analysis Of Internodes)mentioning

confidence: 99%

“…The same arguments used in [21] can be used in the Isogeometric Analysis framework too, to prove the existence, the uniqueness, and the stability of the solution of problem (9).…”

Section: Remark 32 (Analysis Of Internodes)mentioning

confidence: 99%

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The INTERNODES method for the treatment of non-conforming multipatch geometries in Isogeometric Analysis

Gervasio

Marini

2020

Computer Methods in Applied Mechanics and Engineering

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In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. IN-TERNODES is an interpolation-based method that, on each interface of the configuration, exploits two independent interpolation operators to enforce the continuity of the traces and of the normal derivatives. INTERNODES easily handles both parametric and geometric NURBS non-conformity. We specify how to set up the interpolation matrices on non-conforming interfaces, how to enforce the continuity of the normal derivatives and we give special attention to implementation aspects. The numerical results show that INTERNODES exhibits optimal convergence rate with respect to the mesh size of the NURBS spaces an that it is robust with respect to jumping coefficients.

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INTERNODES for Elliptic Problems

Gervasio

Quarteroni

2018

Lecture Notes in Computational Science and Engineering

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Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations

Cited by 15 publications

References 19 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

The INTERNODES method for the treatment of non-conforming multipatch geometries in Isogeometric Analysis

INTERNODES for Elliptic Problems

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