Ensemble Domain Decomposition Algorithm for the Fully-mixed Random Stokes-Darcy Model with the Beavers-Joseph Interface Conditions

TL;DR

This paper introduces an efficient ensemble domain decomposition algorithm for the stochastic Stokes-Darcy model with Beavers-Joseph interface conditions, reducing computational costs while maintaining accuracy through shared matrices and domain decoupling.

Contribution

The paper presents a novel ensemble domain decomposition method that efficiently solves the fully-mixed random Stokes-Darcy model with Beavers-Joseph conditions, featuring shared matrices and optimized convergence.

Findings

Shared coefficient matrices reduce computational cost.

The algorithm achieves convergence rates with optimized Robin parameters.

Numerical experiments validate the efficiency and accuracy of the method.

Abstract

In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully-mixed random Stokes-Darcy model with the physically realistic Beavers-Joseph (BJ) interface conditions. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic Stokes-Darcy numerical models and use the idea of the ensemble to realize the fast computation of multiple problems. One remarkable feature of the algorithm is that multiple linear systems share a common coefficient matrix in each deterministic numerical model, which significantly reduces the computational cost and achieves comparable accuracy with the traditional methods. Moreover, by domain decomposition, we can decouple the Stokes-Darcy system into two smaller sub-physics problems naturally. Both mesh-dependent and mesh-independent convergence rates of the algorithm are rigorously derived by choosing suitable Robin parameters. Optimized Robin parameters are derived and analyzed to accelerate the convergence of the proposed algorithm. Especially, for small hydraulic conductivity in practice, the almost optimal geometric convergence can be obtained by finite element discretization. Finally, two groups of numerical experiments are conducted to validate and illustrate the exclusive features of the proposed algorithm.