A new impedance accounting for short and long range effects in mixed substructured formulations of nonlinear problems

TL;DR

This paper introduces a new heuristic impedance for nonlinear problem solving that effectively combines short and long range effects, enhancing convergence in parallel domain decomposition methods.

Contribution

The paper proposes a novel impedance approximation method that balances efficiency and computational cost for nonlinear structural problems.

Findings

Improved convergence rates in nonlinear domain decomposition methods.

Reduced computational cost for impedance calculation.

Effective handling of short and long range effects in nonlinear problems.

Abstract

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is often too expensive to be computed exactly in practice: an approximate version has to be sought for, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.