On the numerical integration of trimmed isogeometric elements

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Isogeometric analysis for parameterized LSM-based structural topology optimization (2016, background): “To further improve the accuracy, optimal quadrature for arbitrary shapes and topology [44]may replace the density-based”
Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements (2016, methodology): “Nagy and Benson [43] proposed an algorithm to construct efficient quadrature rules for trimmed elements of arbitrary shape and topology, which has been successfully used in multi-trimmed boundary elements [44].”
The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, methodology): “For example, immersed finite element concepts have been employed to resolve multi-phase flow interfaces [7, 31], to deal with trimmed CAD surfaces [17, 50, 61, 65] and image based geometries [62, 68, 69], to prevent mesh updating and mesh distortion [10, 15, 21, 55], or to handle fluid–structure int”