A common numerical problem is computing pairwise interactions between N bodies, where the interactions (your kernel) decay with distance. Any straightforward method is O(N²), quadratic in the number of interactions.
One of the numerical breakthroughs of the past half-century, however, has ben to realize that such computations can often be performed approximately (to any desired accuracy) faster than this, O(N log N) or even O(N). The basic reason is that you don’t need to repeatedly compute interactions between distant bodies, because in distant interactions you can lump nearby bodies together. The most famous such algorithm is the fast multipole method.
So, if you kernel is decaying, then you might be able to use such an algorithm for your underlying problem, whatever that is.
On the other hand, if your kernel(dist) = ifelse(dist <= 100, 1, 0) example function is typical, you can perhaps restrict your search to locations close to the current location. This is called a fixed-radius nearest-neighbor search, and there are various data structures and algorithms to perform such queries efficiently.