Abstract
This chapter focuses on solving elliptic problems by domain decomposition methods with applications. Solving elliptic problems using domain decomposition originates with the classic Schwarz alternating method. Many well-known methods for solving linear systems originating from the approximation of elliptic problems example, block over-relaxation, and block Gauss or Cholesky direct methods take advantage of subdomain decomposition. Used as preconditioners, several variants of the Schwarz method provide efficient tools for solving difficult nonlinear problems on complicated two-dimensional and three-dimensional geometries. The chapter also describes a new domain decomposition method. The two main goals of the method are: (1) find a conjugate gradient variant of the Schwarz's algorithm, and (2) develop some experience of matching methods using least squares. The numerical treatment of nonlinear boundary value problems involving unbounded regions of RN is a nontrivial task.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
