I am looking to perform convolution quadrature, but cannot seem to find any ready-made solution. HCubature.jl and QuadGK.jl seem very capable for ordinary quadrature, but I cannot find any resources for convolution.

To be more precise, this is what I am trying to calculate:

where G is smooth in parts but has several spiky regions, and h is a smoothing function. (\Omega is just a rectangular domain). G is quite expensive to evaluate, so an adaptive scheme like in QuadGK would be very advantageous.

Does anyone know about anything like this? Even something in Matlab or Python?

**Edit:** both h and G are complex-valued, while x,y,z are real-valued, if that makes any difference.