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 [7] provides powerful implementations of a broad variety of well-known numerical methods and algorithms. However, its routines have certain limitations: the numerical integration based on QUADPACK library [2] 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.