Abstract
AbstractIn this paper, we develop a convergence theory for Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch discretizations of the Poisson problem, where the patches are coupled using discontinuous Galerkin. The presented theory provides condition number bounds that are explicit in the grid sizes â and in the spline degrees đ. We give an analysis that holds for various choices for the primal degrees of freedom: vertex values, edge averages, and a combination of both. If only the vertex values or both vertex values and edge averages are taken as primal degrees of freedom, the condition number bound is the same as for the conforming case. If only the edge averages are taken, both the convergence theory and the experiments show that the condition number of the preconditioned system grows with the ratio of the grid sizes on neighboring patches.
Highlights
In this paper, we develop a convergence theory for Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch discretizations of the Poisson problem, where the patches are coupled using discontinuous Galerkin
Isogeometric Analysis (IgA), see [9, 20], is an approach for discretizing partial differential equations (PDEs) that has been developed in order to improve the compatibility between computer aided design (CAD) and simulation in comparison to the standard finite element method (FEM)
In CAD systems, the geometry is usually parameterized in terms of geometry functions which are usually spanned by B-splines or non-uniform rational B-splines (NURBS)
Summary
Isogeometric Analysis (IgA), see [9, 20], is an approach for discretizing partial differential equations (PDEs) that has been developed in order to improve the compatibility between computer aided design (CAD) and simulation in comparison to the standard finite element method (FEM). Convergence Theory for IETI-DP Solvers viously discussed in [24, 25, 38] Such approaches allow the handling of inexact representations of the geometry that yield gaps between or overlaps of neighboring patches, cf [19]. For conforming FEM discretizations, condition number bounds that are explicit in the polynomial degree p have been worked out previously for FETI-DP type, cf [21, 28], other Schwarz type, cf [15, 36], and iterative substructuring methods, cf [2, 29]. The proof follows the abstract framework from [26] and is a continuation of the paper [32], where we have analyzed IETI-DP methods for conforming discretizations.
Sign-in/Register to view highlights & summary 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.
