In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems with Dirichlet and Neumann interface conditions, respectively. After discretization by, e.g., the finite element method, the full-order model (FOM) is solved by Dirichlet-Neumann iterations between the two sub-problems until interface convergence is reached. We then apply the reduced basis (RB) method to obtain a low-dimensional representation of the solution of each sub-problem. Furthermore, we apply the discrete empirical interpolation method (DEIM) at the interface level to achieve a fully reduced-order representation of the DD techniques implemented. To deal with non-conforming FE interface discretizations, we employ the INTERNODES method combined with the interface DEIM reduction. The reduced-order model (ROM) is then solved by sub-iterating between the two reduced-order sub-problems until the convergence of the approximated high-fidelity interface solutions. The ROM scheme is numerically verified on both steady and unsteady coupled problems, in the case of non-conforming FE interfaces.

翻译：本文提出了一种用于处理双向Dirichlet-Neumann参数耦合问题的降阶建模策略，该问题通过区域分解子结构方法求解。我们将原始耦合微分问题分解为两个子问题，分别采用Dirichlet和Neumann界面条件。经有限元法等数值离散后，全阶模型通过两个子问题间的Dirichlet-Neumann迭代求解，直至界面收敛。随后应用缩减基方法获取各子问题解的低维表示。进一步地，我们在界面层级采用离散经验插值方法，以实现所实施区域分解技术的完全降阶表示。针对非一致有限元界面离散问题，我们结合INTERNODES方法与界面DEIM降阶技术进行处理。最终降阶模型通过两个降阶子问题间的迭代求解，直至近似高保真界面解收敛。该降阶模型方案在非一致有限元界面情形下，分别针对稳态与非稳态耦合问题进行了数值验证。