Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

  title={Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries},
  author={Eric B. Chin and N. Sukumar},
  journal={Computer Methods in Applied Mechanics and Engineering},
  • E. Chin, N. Sukumar
  • Published 1 November 2020
  • Mathematics, Computer Science
  • Computer Methods in Applied Mechanics and Engineering

Robust Numerical Integration on Curved Polyhedra Based on Folded Decompositions

Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

Stabilization-free virtual element method for plane elasticity

We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are



An efficient method to integrate polynomials over polytopes and curved solids

Modeling curved interfaces without element‐partitioning in the extended finite element method

  • E. ChinN. Sukumar
  • Computer Science
    International Journal for Numerical Methods in Engineering
  • 2019
This paper model holes and material interfaces in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes and develops an enrichment function that captures weak discontinuities on spectral meshes.

hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of second-order elliptic partial differential equations on general computational meshes consisting of

Scaled boundary parametrizations in isogeometric analysis

Generalized Gaussian quadrature rules on arbitrary polygons

A numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons, which can be used as software libraries where numerical integration within planar polygons is required.

A series of Duffy‐distance transformation for integrating 2D and 3D vertex singularities

The near singularities caused by distorted integral patch/cell shape are revealed numerically and theoretically during the implementation of generalized Duffy transformation, and the Duffy‐distance transformation is developed step by step for the 2D and 3D vertex singularities.

High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles

  • R. Saye
  • Computer Science, Mathematics
    SIAM J. Sci. Comput.
  • 2015
A high-order accurate numerical quadrature algorithm is presented for the evaluation of integrals over curved surfaces and volumes which are defined implicitly via a fixed isosurface of a given