BDDC Deluxe for Isogeometric Analysis

Abstract

The main goal of this paper is to design, analyze, and test a BDDC (Balancing Domain Decomposition by Constraints, see [12, 23]) preconditioner for Isogeometric Analysis (IGA), based on a novel type of interface averaging, which we will denote by deluxe scaling, with either full or reduced set of primal constraints. IGA is an innovative numerical methodology, introduced in [17] and first analyzed in [1], where the geometry description of the PDE domain is adopted from a Computer Aided Design (CAD) parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the same NURBS basis functions are also used as the PDEs discrete basis, following an isoparametric paradigm; see the monograph [10]. Recent works on IGA preconditioners have focused on overlapping Schwarz preconditioners [3, 5, 7, 9], multigrid methods [16], and non-overlapping preconditioners [4, 8, 20].