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- Domain_decomposition_methods abstract "In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. A coarse problem with one or few unknowns per subdomain is used to further coordinate the solution between the subdomains globally. The problems on the subdomains are independent, which makes domain decomposition methods suitable for parallel computing. Domain decomposition methods are typically used as preconditioners for Krylov space iterative methods, such as the conjugate gradient method or GMRES.In overlapping domain decomposition methods, the subdomains overlap by more than the interface. Overlapping domain decomposition methods include the Schwarz alternating method and the additive Schwarz method. Many domain decomposition methods can be written and analyzed as a special case of the abstract additive Schwarz method.In non-overlapping methods, the subdomains intersect only on their interface. In primal methods, such as Balancing domain decomposition and BDDC, the continuity of the solution across subdomain interface is enforced by representing the value of the solution on all neighboring subdomains by the same unknown. In dual methods, such as FETI, the continuity of the solution across the subdomain interface is enforced by Lagrange multipliers. The FETI-DP method is hybrid between a dual and a primal method.Non-overlapping domain decomposition methods are also called iterative substructuring methods.Mortar methods are discretization methods for partial differential equations, which use separate discretization on nonoverlapping subdomains. The meshes on the subdomains do not match on the interface, and the equality of the solution is enforced by Lagrange multipliers, judiciously chosen to preserve the accuracy of the solution. In the engineering practice in the finite element method, continuity of solutions between non-matching subdomains is implemented by multiple-point constraints.Finite element simulations of moderate size models require solving linear systems with millions of unknowns. Several hours per time step is an average sequential run time, therefore, parallel computing is a necessity. Domain decomposition methods embody large potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.".
- Domain_decomposition_methods thumbnail Ddm_original_logo.png?width=300.
- Domain_decomposition_methods wikiPageExternalLink www.ddm.org.
- Domain_decomposition_methods wikiPageExternalLink www.domain-decomposition.com.
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- Domain_decomposition_methods wikiPageWikiLink Abstract_additive_Schwarz_method.
- Domain_decomposition_methods wikiPageWikiLink Additive_Schwarz_method.
- Domain_decomposition_methods wikiPageWikiLink BDDC.
- Domain_decomposition_methods wikiPageWikiLink Balancing_domain_decomposition.
- Domain_decomposition_methods wikiPageWikiLink Balancing_domain_decomposition_method.
- Domain_decomposition_methods wikiPageWikiLink Boundary_value_problem.
- Domain_decomposition_methods wikiPageWikiLink Octave_code.
- Domain_decomposition_methods wikiPageWikiLink Category:Domain_decomposition_methods.
- Domain_decomposition_methods wikiPageWikiLink Coarse_problem.
- Domain_decomposition_methods wikiPageWikiLink Coarse_space_(numerical_analysis).
- Domain_decomposition_methods wikiPageWikiLink Conjugate_gradient_method.
- Domain_decomposition_methods wikiPageWikiLink FETI.
- Domain_decomposition_methods wikiPageWikiLink FETI-DP.
- Domain_decomposition_methods wikiPageWikiLink GMRES.
- Domain_decomposition_methods wikiPageWikiLink Generalized_minimal_residual_method.
- Domain_decomposition_methods wikiPageWikiLink Iterative_method.
- Domain_decomposition_methods wikiPageWikiLink Krylov_space.
- Domain_decomposition_methods wikiPageWikiLink Krylov_subspace.
- Domain_decomposition_methods wikiPageWikiLink Lagrange_multiplier.
- Domain_decomposition_methods wikiPageWikiLink Mathematics.
- Domain_decomposition_methods wikiPageWikiLink Mortar_method.
- Domain_decomposition_methods wikiPageWikiLink Mortar_methods.
- Domain_decomposition_methods wikiPageWikiLink Multigrid_method.
- Domain_decomposition_methods wikiPageWikiLink Multiple-point_constraint.
- Domain_decomposition_methods wikiPageWikiLink Numerical_analysis.
- Domain_decomposition_methods wikiPageWikiLink Numerical_partial_differential_equations.
- Domain_decomposition_methods wikiPageWikiLink Parallel_computing.
- Domain_decomposition_methods wikiPageWikiLink Preconditioner.
- Domain_decomposition_methods wikiPageWikiLink Schwarz_alternating_method.
- Domain_decomposition_methods wikiPageWikiLink File:Ddm_original_logo.png.
- Domain_decomposition_methods wikiPageWikiLinkText "Domain Decomposition".
- Domain_decomposition_methods wikiPageWikiLinkText "Domain decomposition methods".
- Domain_decomposition_methods wikiPageWikiLinkText "decomposition".
- Domain_decomposition_methods wikiPageWikiLinkText "domain decomposition algorithms".
- Domain_decomposition_methods wikiPageWikiLinkText "domain decomposition methods".
- Domain_decomposition_methods wikiPageWikiLinkText "domain".
- Domain_decomposition_methods hasPhotoCollection Domain_decomposition_methods.
- Domain_decomposition_methods wikiPageUsesTemplate Template:Numerical_PDE.
- Domain_decomposition_methods subject Octave_code.
- Domain_decomposition_methods subject Category:Domain_decomposition_methods.
- Domain_decomposition_methods type Method.
- Domain_decomposition_methods type Concept.
- Domain_decomposition_methods comment "In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. A coarse problem with one or few unknowns per subdomain is used to further coordinate the solution between the subdomains globally.".
- Domain_decomposition_methods label "Domain decomposition methods".
- Domain_decomposition_methods sameAs m.03wdk9r.
- Domain_decomposition_methods sameAs Q5289813.
- Domain_decomposition_methods sameAs Q5289813.
- Domain_decomposition_methods wasDerivedFrom Domain_decomposition_methods?oldid=648082112.
- Domain_decomposition_methods depiction Ddm_original_logo.png.
- Domain_decomposition_methods homepage www.ddm.org.
- Domain_decomposition_methods isPrimaryTopicOf Domain_decomposition_methods.