Inexact IETI-DP for conforming isogeometric multi-patch discretizations

TL;DR

This paper introduces an improved IETI-DP method for multi-patch isogeometric discretizations that uses fast diagonalization preconditioners, achieving faster solutions while preserving theoretical condition number bounds.

Contribution

The authors replace sparse LU factorizations with diagonalization preconditioners in IETI-DP, enhancing computational efficiency without losing the proven condition number estimates.

Findings

Faster IETI-DP method achieved with diagonalization preconditioners.

Maintains explicit condition number bounds similar to LU-based approach.

Applicable to conforming multi-patch isogeometric discretizations.

Abstract

In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains with inexact subdomain solvers. Recently, the authors have proven a condition number estimate for a IETI-DP method using sparse LU factorizations for the subdomain problems that is explicit, among other parameters, in the grid size and the spline degree. In the present paper, we replace the sparse LU factorizations by fast diagonalization based preconditioners to get a faster IETI-DP method while maintaining the same explicit condition number bound.