Some Recent Tools and a BDDC Algorithm for 3D Problems in H(curl)

Abstract

We present some recent domain decomposition tools and a BDDC algorithm for 3D problems in the space H(curl; Ω ). Of primary interest is a face decomposition lemma which allows us to obtain improved estimates for a BDDC algorithm under less restrictive assumptions than have appeared previously in the literature. Numerical results are also presented to confirm the theory and to provide additional insights.

FETI‐DP with different scalings for adaptive coarse spaces

“…Definition 2.5 (Deluxe scaling, see, e.g., [6]) By deluxe scaling we refer to the following choice of the scaling matrices:…”

Scalable solvers for complex electromagnetics problems

“…In this work, we will offer some new insights in the definition and construction of the change of basis for the latter general case. As pointed out in [16], the change of variables can be implemented in practice with just a few simple modifications to the standard BDDC algorithm [1].…”

“…The stiffness 2 scaling takes more information into account but can lead to poor preconditioner performance with mildly varying coefficients [24]. A robust approach is the deluxe scaling, first introduced in [16] for 3D problems in curl-conforming spaces. It is based on the solution of local auxiliary Dirichlet problems to compute efficient averaging operators [25,17,26,7,27,28], involving dense matrices per subdomain vertex/edge/face.…”

Dual‐primal isogeometric tearing and interconnecting solvers for multipatch continuous and discontinuous Galerkin IgA equations

“…The analysis of Balancing Domain Decomposition by Constraints (BDDC) preconditioner, which has been done for IgA matrices in [12], also applies to the IETI-DP method due to the same spectrum (with the exception of at most two eigenvalues), see [13]. Based on the FE work in [14], a recent improvement for the IgA BDDC preconditioner with a more advanced scaling technique, the so called deluxe scaling, can be found in [15].…”