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Efficient Pre-Conditioned Iterative Solution Strategies for the Electromagnetic Diffusion in the Earth: Finite-Element Frequency

Source:  Dan Hawkes

ESD geophysicist Evan Um (in collaboration with ESD Geophysics Head Greg Newman and Michael Commer) recently formulated a three-dimensional finite-element-frequency-domain (FEFD) solution for electromagnetic diffusion and efficient solution strategies. A system of FEFD equations is pre-conditioned by incomplete (I) lower/upper (LU) triangular matrices (hence, ILU) and subsequently solved by the quasi-minimal residual (QMR) method. Um et al. demonstrated that when conductivity structures of an earth model and source frequencies are updated/perturbed, ILU computed from the previous model is still an effective and useful pre-conditioner for new forward modelling problems. Using the reusability of ILU, they also proposed a new efficient way to overcome the slow convergence rate of the iterative FEFD solution in the static limit.

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Citation: Um, E., M. Commer, and G. Newman (2013), Efficient pre-conditioned interative solution strategies for the electromagnetic diffusion in the Earth: Finite-element frequency-domain approach. Geophysical Journal International, 193, 1460–1473; DOI:10.1093/gji/ggt071.

Funding: BES, Early Career Development Grant