Nested dissection
= Nested dissection
A <vertex separator> divides the remaining unknowns into disconnected subdomains. Nested dissection recursively eliminates each subdomain before its separator, keeping interaction localized until late in the factorization. For a regular two-dimensional mesh with $N$ unknowns, separators have size $O(\sqrt N)$; the resulting direct factorization uses $O(N^{3/2})$ work and $O(N\log N)$ storage under the usual geometric separator assumptions.