Reducing Computational Costs in 3D Magnetotelluric Simulations via Domain Decomposition and Reduced-Order Modeling

Three-dimensional (3D) Magnetotelluric (MT) probabilistic inversion remains rare in real-world applications because it requires solving the forward problem thousands to millions of times, often making the computational cost prohibitive. Since the total duration of an inversion is directly controlled by the performance of the forward solver, the high computational overhead of 3D MT modeling remains a significant challenge, particularly for large-scale problems requiring high mesh resolutions. To address the poor scaling of existing strategies, we introduce DD–POD, a hybrid framework that integrates Domain Decomposition (DD) with Proper Orthogonal Decomposition (POD). The DD formulation partitions the global problem into subdomains, bypassing the memory limitations of traditional direct solvers and enabling simulations with substantially finer discretizations. Implementing this distributed architecture alone yields simulations that are at least 50% faster than global full-order approaches. Building on this foundation, the integration of POD eliminates the need for repeated large-scale linear system solves within the iterative DD process, delivering total forward-solver speed-ups exceeding 90%. Benchmark experiments and a real-world case study demonstrate that DD–POD consistently outperforms standard global POD strategies in computational efficiency with an acceptable trade-off in numerical accuracy.

(This work was supported by the Marie Sklodowska-Curie Actions (Doctoral Network with Grant agreement No. 101120556))