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 unknowns, separators have size ; the resulting direct factorization uses work and storage under the usual geometric separator assumptions.
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Nested dissection is an algorithmic technique used primarily in numerical linear algebra for solving large sparse systems of linear equations, particularly those arising from finite element methods and related applications. It efficiently exploits the sparse structure of matrices and is particularly suited for problems where the matrix can be partitioned into smaller submatrices.