About: Poincaré–Steklov operator

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In mathematics, a Poincaré–Steklov operator (after Henri Poincaré and Vladimir Steklov) maps the values of one boundary condition of the solution of an elliptic partial differential equation in a domain to the values of another boundary condition. Usually, either of the boundary conditions determines the solution. Thus, a Poincaré–Steklov operator encapsulates the boundary response of the system modelled by the partial differential equation. When the partial differential equation is discretized, for example by finite elements or finite differences, the discretization of the Poincaré–Steklov operator is the Schur complement obtained by eliminating all degrees of freedom inside the domain.

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rdf:type	yago:Ability105616246 yago:Abstraction100002137 yago:Cognition100023271 yago:Know-how105616786 yago:Method105660268 yago:PsychologicalFeature100023100 yago:WikicatDomainDecompositionMethods
rdfs:label	Poincaré–Steklov operator (en)
rdfs:comment	In mathematics, a Poincaré–Steklov operator (after Henri Poincaré and Vladimir Steklov) maps the values of one boundary condition of the solution of an elliptic partial differential equation in a domain to the values of another boundary condition. Usually, either of the boundary conditions determines the solution. Thus, a Poincaré–Steklov operator encapsulates the boundary response of the system modelled by the partial differential equation. When the partial differential equation is discretized, for example by finite elements or finite differences, the discretization of the Poincaré–Steklov operator is the Schur complement obtained by eliminating all degrees of freedom inside the domain. (en)
dcterms:subject	Domain decomposition methods
Wikipage page ID	25561272 (xsd:integer)
Wikipage revision ID	815650763 (xsd:integer)
Link from a Wikipage to another Wikipage	Boundary condition Electrical impedance tomography Normal derivative Vladimir Steklov (mathematician) Mathematics Elliptic partial differential equation Neumann boundary condition Steady-state Vyacheslav Ivanovich Lebedev Heat flux Alberto Calderon Finite differences Dirichlet boundary condition Fluid-structure interaction Schur complement Harmonic function Helmholtz equation Henri Poincaré Temperature Domain decomposition methods Domain (mathematical analysis) Schur complement method Iterative substructuring Finite elements Laplace equation
sameAs	Poincaré–Steklov operator Poincaré–Steklov operator Poincaré–Steklov operator
dbp:wikiPageUsesTemplate	dbt:MathSciNet dbt:Numerical_PDE
has abstract	In mathematics, a Poincaré–Steklov operator (after Henri Poincaré and Vladimir Steklov) maps the values of one boundary condition of the solution of an elliptic partial differential equation in a domain to the values of another boundary condition. Usually, either of the boundary conditions determines the solution. Thus, a Poincaré–Steklov operator encapsulates the boundary response of the system modelled by the partial differential equation. When the partial differential equation is discretized, for example by finite elements or finite differences, the discretization of the Poincaré–Steklov operator is the Schur complement obtained by eliminating all degrees of freedom inside the domain. Note that there may be many suitable different boundary conditions for a given partial differential equation and the direction in which a Poincaré–Steklov operator maps the values of one into another is given only by a convention. (en)
prov:wasDerivedFrom	wikipedia-en:Poincaré–Steklov_operator?oldid=815650763&ns=0
page length (characters) of wiki page	5622 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Poincaré–Steklov_operator
is Link from a Wikipage to another Wikipage of	List of things named after Henri Poincaré Vladimir Steklov (mathematician) List of numerical analysis topics Vyacheslav Ivanovich Lebedev Henri Poincaré Luke's variational principle Schur complement method Poincare–Steklov operator Poincaré-Steklov operator Steklov-Poincare operator Dirichlet-to-Neumann map Dirichlet-to-Neumann operator Dirichlet to Neumann mapping Poincare-Steklov operator Poincare Steklov operator Admittance operator
is Wikipage redirect of	Poincare–Steklov operator Poincaré-Steklov operator Steklov-Poincare operator Dirichlet-to-Neumann map Dirichlet-to-Neumann operator Dirichlet to Neumann mapping Poincare-Steklov operator Poincare Steklov operator Admittance operator
is known for of	Vladimir Steklov (mathematician) Vyacheslav Ivanovich Lebedev
is known for of	Vladimir Steklov (mathematician) Vyacheslav Ivanovich Lebedev
is foaf:primaryTopic of	wikipedia-en:Poincaré–Steklov_operator

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