2015
DOI: 10.1002/nme.5121
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Abstract: SUMMARYA unified strategy for the higher-order accurate integration of implicitly defined geometries is proposed. The geometry is represented by a higher-order level-set function. The task is to integrate either on the zero-level set or in the sub-domains defined by the sign of the level-set function. In three dimensions, this is either an integration on a surface or inside a volume. A starting point is the identification and meshing of the zero-level set by means of higher-order interface elements. For the vo… Show more

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Cited by 132 publications
(143 citation statements)
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References 51 publications
(91 reference statements)
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“…We note that the symmetric Nitsche method with local stabilization parameters seems to be more sensitive to quadrature error, which additionally affects the evaluation of integrals (52) and (53). For a more comprehensive account on the importance of geometrically faithful surface and volume quadrature in immersed finite element methods, we refer the interested reader to a series of of recent papers [28,41,45,47,49,71,74,76]. It is also worthwhile to mention in this context that with the quadrature scheme described, the A matrix of the eigenvalue problem (51) may be nonzero while the B matrix is zero (or vice versa).…”
Section: Laplace Problem: Boundary Conditionsmentioning
confidence: 99%
See 1 more Smart Citation
“…We note that the symmetric Nitsche method with local stabilization parameters seems to be more sensitive to quadrature error, which additionally affects the evaluation of integrals (52) and (53). For a more comprehensive account on the importance of geometrically faithful surface and volume quadrature in immersed finite element methods, we refer the interested reader to a series of of recent papers [28,41,45,47,49,71,74,76]. It is also worthwhile to mention in this context that with the quadrature scheme described, the A matrix of the eigenvalue problem (51) may be nonzero while the B matrix is zero (or vice versa).…”
Section: Laplace Problem: Boundary Conditionsmentioning
confidence: 99%
“…First, they need to be able to evaluate integrals in cut elements. In this context, the importance of geometrically faithful quadrature has been recently highlighted [28,41,45,47,49,71,74,76]. The second component is the enforcement of Dirichlet boundary and interface conditions at immersed boundaries.…”
Section: Introductionmentioning
confidence: 99%
“…zero level sets is discussed in more detail in [36], including the extension to the three-dimensional case.…”
Section: Reconstruction Of the Zero Level Setsmentioning
confidence: 99%
“…Isogeometric shells have been successfully applied for large-deformation analysis [21], in conjunction with various nonlinear material models [22,23], and in contact and fluid-structure interaction problems [24][25][26][27]. On the embedded domain side, the importance of geometrically faithful quadrature of trimmed elements and corresponding techniques have been discussed in a series of recent papers [28,27,[29][30][31][32][33][34][35]. For the weak enforcement of boundary and interface conditions at trimming curves and surfaces, variational methods such as Lagrange multiplier [36][37][38] or Nitsche techniques [39][40][41][42][43][44] have been successfully developed.…”
Section: Introductionmentioning
confidence: 99%