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Domain decomposition methods are widely used and effective in theapproximation of solutions to partial differential equations. Yet the optimalconstruction of these methods requires tedious analysis and is often availableonly in simplified, structured-grid settings, limiting their use for morecomplex problems. In this work, we generalize optimized Schwarz domaindecomposition methods to unstructured-grid problems, using Graph ConvolutionalNeural Networks (GCNNs) and unsupervised learning to learn optimalmodifications at subdomain interfaces. A key ingredient in our approach is animproved loss function, enabling effective training on relatively smallproblems, but robust performance on arbitrarily large problems, withcomputational cost linear in problem size. The performance of the learnedlinear solvers is compared with both classical and optimized domaindecomposition algorithms, for both structured- and unstructured-grid problems.

Learning Interface Conditions in Domain Decomposition Solvers