Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements

By Anand Embar, John Dolbow, I. Harari. 2010

321 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c349579dd72dee0f02b9067f202220b6d8d31c84

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, methodology): “From a range of related approaches that combine the immersed boundary concept with axis-aligned grids of B-spline basis functions [34, 35, 80, 106, 107], we apply the recently introduced B-spline version of the finite cell method [60, 108] to illustrate the benefits of hierarchical refinement in the”
Robust imposition of Dirichlet boundary conditions on embedded surfaces (2012, methodology): “The factor of 2 is chosen to obtain a good performance in computations and is based on previous numerical experience and parametric studies [10, 29].”
Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis (2018, unknown): “Nitsche’s method is adopted for a weak imposition [42].”
Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “Imposing Dirichlet boundary conditions with Nitsche’s method was presented in [123] for spline-based finite elements.”
Thermo-elastic optimization of material distribution of functionally graded structures by an isogeometrical approach (2014, background): “In case of nonhomogeneous boundary conditions, however, this approach may result in significant errors and so various alternative strategies have been proposed (Embar et al., 2010; Liu et al., 2010).”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “Possible technologies are the penalty method [9,55,199], the Lagrange multiplier method [29,55,56,58,59,61,201] or Nitsche’s method [17,30,43,51,53,62,64,66].”
A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, methodology): “Element-wise configuration dependent stabilization parameters can be estimated based on a local eigenvalue problem [40,7,43,44].”
The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, background): “Displacement boundary conditions defined over the Dirichlet boundary D (Figure 1) can be integrated into the discrete system Equation (7) by penalty [9, 25, 26] or variational methods [8, 43, 44].”
A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis (2014, methodology): “In terms of IGA, the Nitsche method was firstly employed in [39] to weakly impose Dirichlet boundary”
Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, methodology): “[41], for good performance in computations, we choose ̨e D 2C 2 I , whereC 2 I is given by the equality sign in Equation (37).”
Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone (2015, background): “[32], with an areafraction tolerance of 1 · 10−6.”
Isogeometric analysis for parameterized LSM-based structural topology optimization (2016, methodology): “Nitsche’s method [22], to deal with the inaccurate loading problems, and improved quadrature for IGA [30] for higher efficiency and accuracy.”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “(17) and (18) by omitting the so-called consistency terms that involve the computation of the normal vector n [59,63].”
The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, methodology): “Suitable stabilization parameters can be estimated by an eigenvalue approach on a global level for the complete mesh [30] or on a local level for each intersected element [25, 26].”