MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A parallel goal-oriented adaptive finite element method for 2.5D electromagnetic modeling

Kerry Key and Jeffrey Ovall


We present a parallel goal-oriented adaptive finite element algorithm that can be used to rapidly compute highly accurate solutions for 2.5D controlled-source electromagnetic (CSEM) and 2D magnetotelluric (MT) modeling problems. We employ unstructured triangular grids to permit efficient discretization of complex modeling domains such as those containing topography, dipping layers and multiple scale structures. Iterative mesh refinement is guided by a goal-oriented error estimator based on a form of dual residual weighting, which is carried out using hierarchical basis computations. Our formulation of the error estimator considers the relative error in the strike aligned fields and their spatial gradients, and therefore results in a more efficient use of mesh vertices than previous error estimators based on absolute field errors. This algorithm is parallelized over frequencies, transmitters, receivers and wave-numbers, where adaptive refinement can be performed in parallel on subsets of these parameters while nearby parameters are able to share the refined grid, thus enabling our algorithm to achieve accurate solutions in run-times of seconds to tens of seconds for realistic models and data parameters when run on cluster computers containing about a thousand processors. Application of this new algorithm to a complex model that includes strong seafloor topography variations and multiple thin stacked reservoirs demonstrates the performance and scalability on a large cluster computer.

marine electromagnetics, adaptive finite elements

Related publications

2011 Repository Open Access
Kerry Key and Jeffrey S. Ovall

A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modeling

In: Geophysical journal international, 186 (2011) 1, pp. 137-154