A Parallel Goal Oriented Adaptive Finite Element Method For 25d Electromagnetic Modeling

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.