Model-order-reduced spectral-element method for high-accuracy and fast 3-D transient electromagnetic forward modeling with SAI-Krylov

With the increasing demand for both accuracy and efficiency in transient electromagnetic (TEM) simulations, conventional 3-D forward modeling methods face growing challenges. This study presents a high-accuracy and high-efficiency 3-D forward modeling approach that combines the spectral-element method (SEM) with a model order reduction (MOR) scheme. High-order orthogonal basis functions are employed, and the computational domain is discretized in a finite-element manner to improve modeling accuracy. During element-level analysis, a reduced-integration strategy is introduced to enhance the sparsity of the double-curl and conductivity matrices, thereby reducing the computational time and memory consumption required for matrix assembly. For temporal treatment, a shift-and-invert Krylov (SAI-Krylov) subspace algorithm is adopted: the basis and projection matrices are constructed using only one matrix factorization and tens of back-substitutions, after which low-dimensional matrix exponential functions are evaluated to efficiently obtain electromagnetic responses at arbitrary times. Comparisons with other numerical methods demonstrate the superior efficiency and accuracy of the proposed approach. Finally, simulations on a 3-D sulfide ore-body model are performed to investigate TEM field propagation for both galvanic and loop sources, confirming the capability of the method to model electromagnetic responses in complex geological settings.