  Operator products occur naturally in a range of regularized boundary integral
equation formulations. However, while a Galerkin discretisation only depends on
the domain space and the test (or dual) space of the operator, products require
a notion of the range. In the boundary element software package Bempp we have
implemented a complete operator algebra that depends on knowledge of the
domain, range and test space. The aim was to develop a way of working with
Galerkin operators in boundary element software that is as close to working
with the strong form on paper as possible while hiding the complexities of
Galerkin discretisations. In this paper, we demonstrate the implementation of
this operator algebra and show, using various Laplace and Helmholtz example
problems, how it significantly simplifies the definition and solution of a wide
range of typical boundary integral equation problems.
