Novel ensemble algorithms for random two-domain parabolic problems

TL;DR

This paper introduces three efficient ensemble algorithms for solving complex random fluid-fluid interaction models, reducing computational costs through shared matrices and parallelization, with proven stability and convergence.

Contribution

The paper presents novel ensemble algorithms that significantly improve computational efficiency for random parabolic problems involving coupled heat equations.

Findings

Algorithms are unconditionally stable and convergent.

Shared coefficient matrices reduce computational costs.

Numerical experiments validate theoretical results and efficiency.

Abstract

In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction parameter due to its complexity and uncertainty. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic fluid-fluid numerical models and use the ensemble idea to realize the fast computation of multiple problems. Our remarkable feature of these algorithms is employing the same coefficient matrix for multiple linear systems, significantly reducing the computational cost. By data-passing partitioned techniques, we can decouple the numerical models into two smaller sub-domain problems and achieve parallel computation. Theoretically, we derive that both algorithms are unconditionally stable and convergent. Finally, numerical experiments are conducted not only to support the theoretical results but also to validate the exclusive feature of the proposed algorithms.