Unified treatment of integrals for curvilinear elements in both finite and boundary element methods

Abstract

In this paper we present the implementation of schemes for handling numerical quadrature for modeling curvilinear elements in both integral and differential equation formulations. The proposed integration schemes are based on singularity cancellation methods that can be extended to curvilinear elements for higher order electromagnetic modeling. The key of the proposed approaches is the introduction of a tangent element. The tangent element not only incorporates fundamental geometry information about the surface, but is also useful in describing bases defined on the element, and facilitates the handling of quadrature rules, especially for singular or near-singular integrals.