An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction

By Axel Gerstenberger, Wolfgang A. Wall. 2008

349 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6b3af731404627cea3192066bdf8c4a30fe9a797

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

Citations in the corpus

Subdivision-stabilised immersed b-spline finite elements for moving boundary flows (2012, methodology): “In the second group, the constraint governing equations are solved with conventional techniques, such as the Lagrange multiplier method [9, 10], the penalty method or the Nitsche method [2, 11, 12].”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “Applications of the XFEM for moderately complex structures interacting with a flow are found in Legay et al. [111], Gerstenberger and Wall [84], and Wagner et al. [194].”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “In case of more complex domains, Dirichlet constraints are defined along boundaries of arbitrary geometry cutting through finite cells, which require an imposition in a weak sense by variational techniques such as the penalty method [56–58], the Lagrange multiplier method [11,21, 59,60] or Nitsche’s”
The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, methodology): “The fictitious domain approach has been widely used in conjunction with penalty methods [9, 10, 11], the mortar approach [12], Lagrange multipliers [8, 13, 14, 15], Nitsche’s method [16], extended finite elements [17, 18, 19, 20], discontinuous Galerkin [21] and spectral methods [22, 23] to address ”
An embedded Dirichlet formulation for 3D continua (2010, neutral): “If the structure surface is given as a discrete mesh, we can couple velocity and displacements into the background mesh without introducing additional intermediate surface meshes as were, for example, required in our original 2D FSI approach [2].”
A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes (2012, background): “See [7, 1, 2, 11, 10, 30, 28] for some examples of the applications of fixed-mesh formulations in time evolving domains.”
Local enrichment of the finite cell method for problems with material interfaces (2013, background): “simulation of evolving discontinuities such as crack propagation [6–8], two-phase fluids [9,10], or fluid-structure interactions [11,12].”
A monolithic Lagrangian approach for fluid–structure interaction problems (2010, methodology): “AsecondoptionwouldrelyonkeepingastandardEulerian formulation for the fluid and a Lagrangian one for the structureallowinganoverlapbetweenthedifferentdomains.Such choiceallowsusingstandardformulationsforeachofthesubdomains and is used, for example, in [14] and [ 15 ].”
Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method (2014, background): “In the past decades, there are a great number of studies concerning the improvement or applications of the X-FEM for various discontinuous problems (Belytschko et al., 2003; Samaniego and Belytschko, 2005; Gerstenberger and Wall, 2008; Zhang et al., 2012; Groß and Reusken, 2007; Sukumar et al., 2001”
Optimal transportation meshfree approximation schemes for fluid and plastic flows (2010, methodology): “A number of strategies have been devised with a view to overcoming this difficulty, including: methods based on continuous remeshing [16–19]; arbitraryLagrangian–Eulerian and related formulations [20–24]; the diffuse element method [25]; meshfree methods (see, e.”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, neutral): “June 28, 2010”