The fellowship grant from the Graduate School of Geosciences gave me the opportunity to continue the work on my PhD project and present a part of the work on an international workshop.
A novel meshfree three-dimensional algorithm to calculate the approximate solution of Maxwell’s equations on a bounded simulation domain was developed in this time. The goal was the application to simulate magnetotelluric responses for a given three-dimensional conductivity structure. To derive a stable approximation for Maxwell’s equations a potential approach utilizing a damped Lorentz gauge was used, which results in a weakly coupled system of differential equations. In contrast to other numerical approximation schemes like finite element or finite difference formulations, no connected mesh or grid is needed to calculate the solution. To derive a spatial discretization for the partial differential equations, we use a generalized moving least squares approximation coupled with a collocation scheme. This approximation can be used on general, unordered point clouds to derive a linear system of equations corresponding to the approximate solution of differential equations.
This method is a completely new way to model geophysical, electromagnetic data and has been presented for the first time.
During the three month of the GSGS Fellowship Grant, final implementations and simulations have been done. In the last part of this grant, the work was prepared for presenting at an international workshop held in Berkeley, USA.
Extended abstract:
J. Wittke, B. Tezkan; Three-dimensional meshless magnetotelluric modeling. 6th International Symposium on Three-Dimensional Electromagnetics, Berkeley, California, March 28–30, 2017
Jan Wittke
PhD student
Institute of Geophysics & Meteorology
PhD project: “Meshfree modeling and inversion of magnetotelluric data”
Thesis: Meshless methods for Maxwell’s equations with applications to
magnetotelluric modelling and inversion
Supervisor: Professor Dr. Bülent Tezkan
Defense: 16 November 2017