  We study the effect of localized attacks on a multiplex spatial network,
where each layer is a network of communities. The system is considered
functional when the nodes belong to the giant component in all the multiplex
layers. The communities are of linear size $\zeta$, such that within them any
pair of nodes are linked with same probability, and additionally nodes in
nearby communities are linked with a different (typically smaller) probability.
This model can represent an interdependent infrastructure system of cities
where within the city there are many links while between cities there are fewer
links. We develop an analytical method, similar to the finite element method
applied to a network with communities, and verify our analytical results by
simulations. We find, both by simulation and theory, that for different
parameters of connectivity and spatiality --- there is a critical localized
size of damage above which it will spread and the entire system will collapse.
