Efficient and accurate simulation of electromagnetic responses of geologically-rich geophysical settings is crucial in a variety of scenarios, including mineral and petroleum exploration, water resource utilizations, and geothermal power extractions. In this talk, we develop two multiscale methods to compute such type of responses in a numerically effective manner.
Geophysical electromagnetic simulations of highly heterogeneous media are computationally expensive. One major reason for this is the fact that very fine meshes are often required to accurately discretize the physical properties of the media, which may vary over a wide range of spatial scales and several orders of magnitude. Using such fine meshes for the discrete models leads to solve large systems of equations that are often difficult to deal with. To reduce the computational cost of the electromagnetic simulation, we develop multiscale methods for the quasi-static Maxwells equations in the frequency domain.
Our methods begin by locally computing multiscale basis functions, which incorporate the small-scale information contained in the physical properties of the media. Using a Galerkin proper orthogonal decomposition approach, the local basis functions are then used to represent the solution on a coarse mesh. Our approach leads to a significant reduction in the size of the final system of equations to be solved and in the amount of computational time of the simulation, while accurately approximating the behavior of the fine-mesh solutions. We demonstrate the performance of our methods in the context of an application in mining exploration.
This work is done in collaboration with Prof. Eldad Haber (UBC), Dr. Wenke Wilhelms (UBC), and Dr. Christoph Schwarzbach (Computational Geosciences).