Neumann–Dirichlet method

In mathematics, the Neumann–Dirichlet method is a domain decomposition preconditioner which involves solving Neumann boundary value problem on one subdomain and Dirichlet boundary value problem on another, adjacent across the interface between the subdomains.^[1] On a problem with many subdomains organized in a rectangular mesh, the subdomains are assigned Neumann or Dirichlet problems in a checkerboard fashion.

References[]

^ O. B. Widlund, Iterative substructuring methods: algorithms and theory for elliptic problems in the plane, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), SIAM, Philadelphia, PA, 1988, pp. 113–128.

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[Widlund-1988-ISM-1] O. B. Widlund, Iterative substructuring methods: algorithms and theory for elliptic problems in the plane, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), SIAM, Philadelphia, PA, 1988, pp. 113–128.

[1]

Neumann–Dirichlet method

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