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.

Numerical partial differential equations

Finite difference methods	Heat Equation and related: FTCS scheme · Crank–Nicolson method Hyperbolic: Lax–Friedrichs method · Lax–Wendroff method · MacCormack method · Upwind scheme · Other: Alternating direction implicit method · Finite-difference time-domain method

Finite volume methods	Godunov's scheme · High-resolution scheme · MUSCL scheme · AUSM · Riemann solver

Finite element methods	hp-FEM · Extended finite element method · Discontinuous Galerkin method · Spectral element method · Meshfree methods · Mortar methods

Other methods	Spectral method · Pseudospectral method · Method of lines · Multigrid methods · Collocation method · Level set method · Boundary element method · Immersed boundary method · Analytic element method · Particle-in-cell · Isogeometric analysis

Domain decomposition methods	Schur complement method · Fictitious domain method · Schwarz alternating method · Additive Schwarz method · Abstract additive Schwarz method · Neumann–Dirichlet method · Neumann–Neumann methods · Poincaré–Steklov operator · Balancing domain decomposition · BDDC · FETI · FETI-DP

‹The stub template below has been proposed for renaming to . See stub types for deletion to help reach a consensus on what to do.
Feel free to edit the template, but the template must not be blanked, and this notice must not be removed, until the discussion is closed. For more information, read the guide to deletion.›

Neumann–Dirichlet method

See also

References