Metagraph-Based Domain-Decomposed Galerkin Reduced-Order Model

This study proposes a metagraph-based domain-decomposed Galerkin reduced-order model (MBDD-G-ROM) for distributed-memory parallel reduced-order analysis of large-scale problems.

The method represents domain-decomposed Galerkin reduced-order models over arbitrary domain decompositions using two graph levels: calculation-point graphs for interactions among discretization points and metagraphs for connectivity among local approximation-space subdomains.

In the proper orthogonal decomposition (POD)-based implementation, POD computation subdomains are represented as metanodes, while metaedges encode the block-sparsity induced by overlaps between local POD basis supports.

Partitioning the metagraph enables the POD computation subdomains to be decoupled from the parallel computation subdomains, allowing distributed-memory parallelization of both offline and online phases, including reduced-system assembly and iterative linear solution, without requiring the two decompositions to coincide.

The metagraph also supports static load balancing through metanode weights that approximate computational costs.

The method is evaluated for an unsteady diffusion equation and incompressible Navier-Stokes flow around a three-dimensional cylinder.

The results show that MBDD-G-ROM preserves reduced-order solution accuracy while achieving high online parallel efficiency.

A load-balancing test further demonstrates that cost-based metanode weights can improve computational efficiency.