Generalized Gaussian quadrature rules on arbitrary polygons

By S. Mousavi, Hong Xiao, Natarajan Sukumar. 2010

193 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/71941e9cda397397c11763da07bd9ce02f5a3d53

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection (2013, methodology): “First, few tailored quadrature schemes are available in the literature owing to the arbitrary geometry of the element domain (see [25, 26] and references therein).”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “Here, we generalize the algorithm in Reference [36] to develop quadrature rules for piecewise polynomials on finite elements that are intersected by kinked cracks.”
Polygonal finite elements for topology optimization: A unifying paradigm (2010, unknown): “Alternatively, numerical integration can be carried out using special quadrature rules developed for polygonal domains (see, for example, [30–32]).”
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods (2015, methodology): “Other possible approaches include complex mappings such as the Schwarz–Christoffel conformal mapping [41, 54]; adaptively weighted numerical integration scheme [55]; generalized Gaussian quadrature rules [42]; and Guass–Green cubature [56], to name a few.”
On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations (2012, background): “[17] and Xiao and Gimbutas [20], propose an interesting technique and certainly deserves more attention.”
Generalized Duffy transformation for integrating vertex singularities (2009, methodology): “[59] to construct a very efficient quadrature rule with far fewer number of evaluation points.”
New perspectives on polygonal and polyhedral finite element methods (2014, methodology): “In polygonal finite element computations, on partitioning each n-gon into n triangles, and using standard polynomial-precise quadrature rules in each triangle, the patch test is only met to 10−4–10−8 accuracy [39, 132].”
Segment-based vs. element-based integration for mortar methods in computational contact mechanics (2015, methodology): “First, the position and the weighting of each integration point could be calculated for each integration domain individually by using a moment-fitting related approach [26,27,52] or by employing methods based on the divergence theorem [42–44].”
An efficient augmented finite element method for arbitrary cracking and crack interaction in solids (2014, background): “[60], six Gaussian points are needed to integrate the stiffness matrix with sufficient numerical accuracy.”