Reduced Order Modeling for Domain Decomposition: A Structured Review of Methods and Applications
Researchers have published a structured review on arXiv examining methods that combine Reduced Order Models (ROMs) with Domain Decomposition (DD) techniques to accelerate computational fluid dynamics simulations. The paper categorizes existing approaches into intrusive (projection-based) and non-intrusive (data-driven) frameworks, detailing strategies for building and coupling local reduced models across subdomains. The work aims to consolidate a rapidly growing field and identify open challenges for future engineering applications.
A preprint posted to arXiv (math.NA / physics.flu-dyn) presents a structured literature review of methods that integrate Reduced Order Models with Domain Decomposition techniques in computational fluid dynamics. The authors argue that many industrial geometries contain repeating or physically distinct subregions, making them natural candidates for DD approaches, and that pairing DD with ROMs can substantially reduce computational costs compared to conventional high-fidelity CFD. The review organizes existing methodologies into two broad categories: intrusive, projection-based methods—covered in technical depth including governing equations and numerical algorithms—and non-intrusive, data-driven methods, for which general procedures and underlying principles are outlined. Particular attention is given to strategies for generating local reduced bases and coupling them across subdomain interfaces to form coherent global solutions. The paper concludes by summarizing the current state of the literature, cataloguing open challenges such as interface coupling accuracy and scalability, and offering perspectives on future implementation from an engineering standpoint. The preprint was first submitted in January 2026 and revised in June 2026.
What's missing
As a preprint review article, this work has not yet undergone formal peer review, which limits confidence in the completeness and balance of the literature surveyed. The abstract does not specify the number of papers reviewed, the time span of literature covered, or the criteria used for inclusion and exclusion of studies. Quantitative benchmarks comparing the computational savings achieved by ROM-DD methods versus full-order models are not described in the abstract, leaving the magnitude of claimed efficiency gains unverified.
What different sources said
- arXiv physicsCenter
A Structured Review of Reduced Order Modeling for Domain Decomposition Problems: State of the Art and Perspectives
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