Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces

TL;DR

This paper introduces a reduced order modeling approach combining RB and DEIM to efficiently solve parametrized one-way coupled problems with non-conforming interfaces, enabling faster analysis of complex multi-physics systems.

Contribution

It presents a novel ROM technique that handles non-conforming interfaces in coupled problems using DEIM-based data projection, extending reduced modeling to complex interface scenarios.

Findings

Effective reduction in computational cost demonstrated.

Accurate solutions with a-posteriori error estimates.

Applicable to steady and unsteady coupled problems.

Abstract

One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domains discretizations employed. Moreover, very often complex submodels depend on (e.g., physical or geometrical) parameters. Understanding how outputs of interest are affected by parameter variations thus plays a key role to gain useful insights on the problem's physics; however, expensive repeated solutions of the problem using high-fidelity, full-order models are often unaffordable. In this paper, we propose a parametric reduced order modeling (ROM) technique for parametrized one-way coupled problems made by a first independent model, the master model, and a second model, the slave model, that depends on the master model through Dirichlet interface conditions. We combine a reduced basis (RB) method, applied to each subproblems, with the discretized empirical interpolation method (DEIM) to efficiently interpolate or project Dirichlet data across conforming and non-conforming meshes at the domains interface, building a low-dimensional representation of the overall coupled problem. The proposed technique is then numerically verified by considering a series of test cases involving both steady and unsteady problems, and deriving a-posteriori error estimates on the solution of the coupled problem in both cases. This work arises from the need to solve staggered cardiac electrophysiological models and represents the first step towards the setting of ROM techniques for the more general two-way Dirichlet-Neumann coupled problems solved with domain decomposition sub-structuring methods, when interface non-conformity is involved.