Machine Learning Enhanced Boundary Element Method: Prediction of Gaussian Quadrature Points

The Gaussian Quadrature Method

Extrapolation-based Boundary Element Quadrature

Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, and the Boundary Element Method

This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes. AMS Subject Classfication: 65D30, 65D32, 65N38.

Generalized Gaussian Quadrature Rules in Enriched Finite Element Methods

In this paper, we present new Gaussian integration schemes for the efficient and accurate evaluation of weak form integrals that arise in enriched finite element methods. For discontinuous functions we present an algorithm for the construction of Gauss-like quadrature rules over arbitrarily-shaped elements without partitioning. In case of singular integrands, we introduce a new polar transforma...

Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method

New Gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method. For discontinuous functions, we construct Gauss-like quadrature rules over arbitrarily-shaped elements in two dimensions without the need for partitioning the finite element. A point elimination algorithm is used in the construction of the quadra...