Quadrature for second-order triangles in the Boundary Element Method

TL;DR

This paper introduces a quadrature technique for second-order curved triangles in the Boundary Element Method, utilizing polar coordinate transformation and geometric operations, with demonstrated numerical accuracy on Laplace equation solutions.

Contribution

It presents a novel quadrature method specifically designed for second-order curved triangles in BEM, improving numerical integration accuracy.

Findings

Error of order P^{-1.6} demonstrated on Laplace problem

Method effective for curved second-order triangles

Numerical results validate the approach

Abstract

A quadrature method for second-order, curved triangular elements in the Boundary Element Method (BEM) is presented, based on a polar coordinate transformation, combined with elementary geometric operations. The numerical performance of the method is presented using results from solution of the Laplace equation on a cat's eye geometry which show an error of order $P^{-1.6}$, where $P$ is the number of elements.