Reducing the Computational Burden of Large-Scale Geophysical Simulations via Domain Decomposition and Model Order Reduction: A 3D Magnetotelluric Application
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Simulation-based engineering for high-dimensional, large-scale geophysical systems faces the challenge of immense computational costs, particularly within frameworks that require repeated high-fidelity simulations. In this context, standard solvers for large-scale linear systems often become intractable due to memory bottlenecks and prohibitively long runtimes. A prominent example is 3D Magnetotellurics (MT), a geophysical method that requires solving Maxwell's equations over complex domains to deliver high-resolution outputs. To address this, we present a more efficient forward-modelling framework that couples iterative Domain Decomposition (DD) with Model Order Reduction (MOR) based on Proper Orthogonal Decomposition (POD). The DD component partitions the high-dimensional global system into manageable subdomains, circumventing the memory limitations associated with direct global factorization. Subsequently, the MOR component constructs a reduced basis from local DD snapshots, creating a reduced-order version of the problem that can deliver accurate and fast solutions during subsequent evaluations. We validate this approach using standard academic benchmarks and a complex real-world conductivity model, scaling the problem up to $2 \times 10^7$ degrees of freedom. The proposed DD--POD framework achieves computational speed-ups exceeding 90\% relative to full-order solvers and up to 70\% relative to existing ROM techniques, while maintaining acceptable accuracy.
