World Library  
Flag as Inappropriate
Email this Article

Schwarz alternating method

Article Id: WHEBN0016252015
Reproduction Date:

Title: Schwarz alternating method  
Author: World Heritage Encyclopedia
Language: English
Subject: Domain decomposition methods, Neumann–Neumann methods, Abstract additive Schwarz method, Neumann–Dirichlet method, Fictitious domain method
Publisher: World Heritage Encyclopedia

Schwarz alternating method

In mathematics, the Schwarz alternating method, named after Hermann Schwarz, is an iterative method to find the solution of a partial differential equations on a domain which is the union of two overlapping subdomains, by solving the equation on each of the two subdomains in turn, taking always the latest values of the approximate solution as the boundary conditions. A modification of the method, known as the additive Schwarz method, has become a practical domain decomposition method. An abstract formulation of the original method is then referred to as the multiplicative Schwarz method.

Historical notice

It was first formulated by H. A. Schwarz [1] and served as a theoretical tool: its convergence for general second order elliptic partial differential equations was first proved much later, in 1951, by Solomon Mikhlin.[2]

See also


  1. ^ See his paper (Schwartz 1870)
  2. ^ See the paper (Mikhlin 1951): a comprehensive exposition was given by the same author in later books


  • .
  • .

External links

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.