Numerical integration of two-dimensional complex-valued functions for the needs of BIEM

Abstract

Numerical integration is a key problem with numerous applications, including the boundary integral equation method (BIEM). GSL \cite{Gough2009} provides powerful implementations of broad variety of well-known numerical methods and algorithms. However, its routines have certain limitations: the numerical integration based on QUADPACK library \cite{Piessens1983} is implemented only in the case of one-dimensional functions.

In this paper we present an extension of the GSL numerical integration routines for the special case of two-dimensional complex-valued functions. The presented approach is part of our effort to build a BIEM software system for solving a 3D elastodynamics problem for wave propagation in a continuously inhomogeneous half-space.