Abstract
The main obstacle for obtaining fast domain decomposition solvers for spectral element discretizations of second order elliptic equations was the lack of fast solvers for local internal problems on subdomains of decomposition and their faces. As recently shown by Korneev and Rytov, such solvers can be derived on the basis of a specific interrelation between stiffness matrices of the spectral and hierarchical p reference elements (coordinate polynomials of the latter are tensor products of the integrated Legendre’s polynomials). This interrelation allows us to develop fast solvers for discretizations by spectral elements, which are quite similar in basic features to those developed for discretizations by hierarchical elements. Using these facts and preceding findings on the wire basket preconditioners, we present a domain decomposition preconditioner-solver for spectral element discretizations of second order elliptic equations in 3-d domains which is almost optimal in the total arithmetical cost.
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 callMore From: Computer Methods in Applied Mechanics and Engineering
Disclaimer: 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.
