Abstract additive Schwarz method
Encyclopedia
In mathematics
, the abstract additive Schwarz method, named after Hermann Schwarz
, is an abstract version of the additive Schwarz method, formulated only in terms of linear algebra
without reference to domains, subdomains, etc. Many if not all domain decomposition methods
can be cast as abstract additive Schwarz method, which is often the first and most convenient approach to their analysis.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the abstract additive Schwarz method, named after Hermann Schwarz
Hermann Schwarz
Karl Hermann Amandus Schwarz was a German mathematician, known for his work in complex analysis. He was born in Hermsdorf, Silesia and died in Berlin...
, is an abstract version of the additive Schwarz method, formulated only in terms of linear algebra
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
without reference to domains, subdomains, etc. Many if not all domain decomposition methods
Domain decomposition methods
]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...
can be cast as abstract additive Schwarz method, which is often the first and most convenient approach to their analysis.