Abstract

A BDDC (Balancing Domain Decomposition by Constraints) algorithm for a staggered discontinuous Galerkin approximation is considered. After applying domain decomposition method, a global linear system on the subdomain interface unknowns is obtained and solved by the conjugate gradient method combined with a preconditioner. To construct a preconditioner that is robust to the coefficient variations, a generalized eigenvalue problem on each subdomain interface is solved and primal unknowns are selected from the eigenvectors using a predetermined tolerance. By the construction of the staggered discontinuous Galerkin methods, the degrees of freedom on subdomain interfaces are shared by only two subdomains, and hence the construction of primal unknowns are simplified. The resulting BDDC algorithm is shown to have the condition number bounded by the predetermined tolerance. A modified algorithm for parameter dependent problems is also introduced, where the primal unknowns are only computed in an offline stage. Numerical results are included to show the performance of the proposed method and to verify the theoretical estimate.

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 call

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.