A multiscale method for fast electromagnetic simulations

Abstract

Simulating low-frequency electromagnetic fields by solving Maxwell’s equations is a central task in many geophysical applications. In most cases, geophysical targets of interest exhibit complex topography and bathymetry as well as layers and faults. Capturing these effects accurately in numerical simulations is challenging. Standard approaches require a very fine discretization that can result in an impracticably large linear system to be solved. A remedy is to use locally refined and adaptive meshes, however, the potential coarsening is limited in the presence of highly heterogeneous and anisotropic conductivities. In this paper we discuss the application of Multiscale Finite Volume (MSFV) methods to Maxwell’s equations in frequency domain. Given a partition of the fine mesh into a coarse mesh the idea is to obtain coarse-to-fine interpolation by solving local versions of Maxwell’s equations on each coarsened grid cell. By construction, the interpolation accounts for fine scale conductivity changes, yields a natural homogenization, and reduces the fine mesh problem dramatically in size. We show that using MSFV methods we can simulate electromagnetic fields with reasonable accuracy in a fraction of the time as compared to state-of-the-art solvers for the fine mesh problem, especially when considering parallel platforms.