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.

ACM Computing Classification System (1998): G.1, G.4.

Key words: numerical integration, two-dimensional complex-valued functions,
GSL C++ wrapper.

This work is supported by research Grant IB-RA2014-178-EnTranEmiss from
the Federal Ministry of Education Research in Germany.