A Multiscale Finite Volume Method with Oversampling for Geophysical Electromagnetic Simulations

Abstract

on, we develop a Multiscale finite volume (MSFV) method with oversampling for the quasistatic Maxwell’s equations in the frequency domain. Our method begins by assuming a coarse mesh nested into a fine mesh, which accurately discretizes the setting. For each coarse cell, we solve independently a local version of the original Maxwell’s system subject to linear boundary conditions on an extended domain, which includes the coarse cell and a neighborhood of fine cells around it. To solve the local Maxwell’s system, we use the fine mesh contained in the extended domain and the Mimetic Finite Volume method. Afterwards, these local solutions, called basis functions, together with a weak continuity condition are used to construct a coarse-scale version of the global problem that is much cheaper to solve. The basis functions can be used to obtain the fine-scale details from the solution to the coarse-scale problem. 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 method using a heterogeneous 3D mineral deposit model.