A new Algorithm Based on Factorization for Heterogeneous Domain Decomposition

TL;DR

This paper introduces a factorization-based heterogeneous domain decomposition algorithm for advection-reaction-diffusion problems, enabling efficient solutions that closely approximate viscous solutions while solving simpler inviscid models in parts of the domain.

Contribution

The paper presents a novel factorization algorithm for heterogeneous domain decomposition, improving accuracy over existing methods for advection-reaction-diffusion problems.

Findings

Achieves solutions close to fully viscous models with reduced computational cost

Provides detailed error analysis demonstrating improved accuracy

Outperforms existing heterogeneous domain decomposition algorithms

Abstract

Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection reaction diffusion type a heterogeneous domain decomposition algorithm which allows us to recover a solution that is very close to the solution of the fully viscous problem, but solves only an inviscid problem in parts of the domain. Our new algorithm is based on the factorization of the underlying differential operator, and we therefore call it factorization algorithm. We give a detailed error analysis, and show that we can obtain approximations in the viscous region which are much closer to the viscous solution in the entire domain of simulation than approximations obtained by other heterogeneous domain decomposition algorithms from the literature.