Improved recovery of admissible stress in domain decomposition methods - application to heterogeneous structures and new error bounds for FETI-DP

TL;DR

This paper enhances the recovery of admissible stress fields in domain decomposition methods, especially for heterogeneous structures, and introduces new error bounds for FETI-DP, improving accuracy and efficiency in structural analysis.

Contribution

It presents a novel approach for admissible stress recovery, optimized for heterogeneous structures, and derives new error bounds for FETI-DP and BDDC methods.

Findings

Improved stress recovery technique for substructured problems.

Minimized error estimators in heterogeneous structures.

New error bounds for FETI-DP and BDDC methods.

Abstract

This paper investigates the question of the building of admissible stress field in a substructured context. More precisely we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), (3) a procedure to build admissible fields for FETI-DP and BDDC methods leading to an error bound which separates the contributions of the solver and of the discretization.