In mathematics, the Neumann–Dirichlet method is a
domain decomposition preconditioner
In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing ...
which involves solving
Neumann
Neumann () is a German language, German surname, with its origins in the pre-7th-century (Old English) word ''wikt:neowe, neowe'' meaning "new", with ''wikt:mann, mann'', meaning man. The English form of the name is Newman. Von Neumann is a varian ...
boundary value problem
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satis ...
on one subdomain and
Dirichlet
Johann Peter Gustav Lejeune Dirichlet (; ; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved special cases of Fermat's last theorem and created analytic number theory. In Mathematical analysis, analysis, h ...
boundary value problem
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satis ...
on another, adjacent across the interface between the subdomains.
[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.] On a problem with many subdomains organized in a rectangular mesh, the subdomains are assigned Neumann or Dirichlet problems in a checkerboard fashion.
See also
*
Neumann–Neumann method
References
Domain decomposition methods
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