Coupling deal.II and FROSch: A Sustainable and Accessible (O)RAS Preconditioner

TL;DR

This paper presents a new software interface coupling deal.II with FROSch to efficiently solve complex PDE systems using RAS and ORAS preconditioners, demonstrating good performance in challenging fluid-structure and Maxwell's equations problems.

Contribution

A novel Tpetra-based interface for coupling deal.II with FROSch, including the newly added ORAS preconditioner, applicable to various finite element types and complex PDE models.

Findings

FROSch-deal.II interface is straightforward and user-friendly.

Preconditioners perform well on nonlinear, nonstationary PDEs.

Numerical experiments confirm solver efficiency in 2D and 3D.

Abstract

In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and FROSch is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to FROSch. The FROSch-deal.II interface works for both Lagrange-based and N\'ed\'elec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell's equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the FROSch-deal.II interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.