  We present an extension of the AAA (adaptive Antoulas--Anderson) algorithm
for periodic functions, called 'AAAtrig'. The algorithm uses the key steps of
AAA approximation by (i) representing the approximant in (trigonometric)
barycentric form and (ii) selecting the support points greedily. Accordingly,
AAAtrig inherits all the favourable characteristics of AAA and is thus
extremely flexible and robust, being able to consider quite general sets of
sample points in the complex plane. We consider a range of applications with
particular emphasis on solving Laplace's equation in periodic domains and
compressing periodic conformal maps. These results reproduce the tapered
exponential clustering effect observed in other recent studies. The algorithm
is implemented in Chebfun.

Numerical Analysis;Numerical Analysis