Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons

Authors:
S. E. Mousavi;N. Sukumar
Affiliations:
Department of Civil and Environmental Engineering, University of California, Davis, USA 95616;Department of Civil and Environmental Engineering, University of California, Davis, USA 95616
Venue:
Computational Mechanics
Year:
2011

Citing 10
Cited 6

Moderate-degree tetrahedral quadrature formulas

Computer Methods in Applied Mechanics and Engineering
Boundary integration over linear polyhedra

Computer-Aided Design
Integration of polynomials over n-dimensional polyhedra

Computer-Aided Design - Beyond solid modelling
Exact integrations of polynomials and symmetric quadrature formulas over arbitrary polyhedral grids

Journal of Computational Physics
Fast and accurate computation of polyhedral mass properties

Journal of Graphics Tools
Flexible simulation of deformable models using discontinuous Galerkin FEM

Graphical Models
Mimetic finite difference method for the Stokes problem on polygonal meshes

Journal of Computational Physics
A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions

Computers & Mathematics with Applications
Polyhedral finite elements using harmonic basis functions

SGP '08 Proceedings of the Symposium on Geometry Processing
Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes

SIAM Journal on Numerical Analysis

LLM and X-FEM based interface modeling of fluid---thin structure interactions on a non-interface-fitted mesh

Computational Mechanics
Simulation of finite-width process zone in concrete-like materials by means of a regularized extended finite element model

Computational Mechanics
Local enrichment of the finite cell method for problems with material interfaces

Computational Mechanics
Mimetic finite difference method

Journal of Computational Physics
FEM with Trefftz trial functions on polyhedral elements

Journal of Computational and Applied Mathematics
Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.02

Visualization

Abstract

We construct efficient quadratures for the integration of polynomials over irregular convex polygons and polyhedrons based on moment fitting equations. The quadrature construction scheme involves the integration of monomial basis functions, which is performed using homogeneous quadratures with minimal number of integration points, and the solution of a small linear system of equations. The construction of homogeneous quadratures is based on Lasserre's method for the integration of homogeneous functions over convex polytopes. We also construct quadratures for the integration of discontinuous functions without the need to partition the domain into triangles or tetrahedrons. Several examples in two and three dimensions are presented that demonstrate the accuracy and versatility of the proposed method.