Universität zu Köln

Wittke, Jan (2017). Meshless methods for Maxwell’s equations with applications to magnetotelluric modelling and inversion. PhD thesis, Universität zu Köln.

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Abstract

The first part of thesis presents new meshless methods for solving time harmonic electromagnetic fields in closed two- or three-dimensional volumes containing heterogeneous materials. This new methods will be used to simulate magnetotelluric experiments, when an Earth conductivity model is given in advanced. Normally, classical approximation methods like finite elements or finite differences are used to solve this task. The algorithms here in this thesis, only need an unstructured point sampling in the modelling domain for the discretization and is able to gain a solution for the partial differential equation without a fixed mesh or grid. This is advantageous when complex model geometries have to be described, because no adapted mesh or grid need to be generated. The meshless methods, described here in this thesis, use a direct discretization technique in combination with a generalized approximation method. This allows to formulate the partial differential equations in terms of linear functionals, which can be approximated and directly form the discretization. For the two-dimensional magnetotelluric problem, a second-order accurate algorithm to solve the partial differential equations was developed and tested with several example calculations. The accuracy of the new meshless methods was compared to analytical solutions, and it was found, that a better accuracy can be achieved with less degrees of freedoms compared to previously published results. For the three-dimensional case, a meshless formulation was given and numerical calculations show the ability of the scheme to handle models with heterogeneous conductivity structures. In the second part of this thesis, the newly developed two-dimensional simulation method will be used in an inversion scheme. Here, the task is to recover the unknown Earth conductivity model with the help of data gained from a magnetotelluric experiment. Due to the previously developed meshless approximation algorithm, some numerical tasks during the inversion can be simplified by reusing the discretization defined on the point sampling from the forward simulation. The newly developed meshless inversion algorithm will be tested with synthetic data to reconstruct known conductivity anomalies. It can be shown, that the inverse algorithm produces correct results, even in the presence of topography.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Wittke, Jan wittke@geo.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-79072
Date:	29 November 2017
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Geosciences > Institute for Geophysics and Meteorology
Subjects:	Mathematics Physics Earth sciences
Uncontrolled Keywords:	Keywords Language magnetotellurik, nummerik, partielle Differentialgleichung, gitterfreie Methoden, Inversion German magnetotellurics, meshfree methods, partial differential equations, inversion UNSPECIFIED
Date of oral exam:	16 November 2017
Referee:	Name Academic Title Tezkan, Bülent Prof. Dr. Spitzer, Klaus Prof. Dr. Michael, Becken Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/7907