Balancing domain decomposition by constraints associated with subobjects. (January 2019)

• Record Type: Journal Article
• Authors: Badia, Santiago; Martín, Alberto F.; Nguyen, Hieu
• Is Part Of: Applied mathematics letters. Volume 87(2019)
• Page Start: 93
• Page End: 100
• Publication Date: 2019-01
• Subjects: BDDC -- FETI-DP -- Optimal preconditioner -- Parallel solver -- Heterogeneous problems; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.07.033
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by C ( 1 + log ( L ∕ h ) ) 2, where C is a constant, and h and L are the characteristic sizes of the mesh and the subobjects, respectively. As L can be chosen almost freely, the condition number can theoretically be as small as O ( 1 ) . We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.