Distributed finite element solution using model order reduction

2024/04/09 by Gustafsson, Tom, Hannukainen, Antti, Kohonen, Vili
#65F55 #65N30 #65N55 #65Y05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2404.06260

Abstract

We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices and optimal reduced bases. A memory-efficient methodology is proposed to project the global finite element linear system onto the reduced basis. Our numerical results demonstrate the technique using non-trivial tetrahedral meshes and subdomain interfaces with up to 85 million degrees-of-freedom on a laptop computer by distributing the bulk of the model order reduction to the cloud.

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