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

We present a parallel goal-oriented adaptive finite element method that can be used to rapidly compute highly accurate solutions for 2.5-D controlled-source electromagnetic (CSEM) and 2-D magnetotelluric (MT) modelling problems. We employ unstructured triangular grids that permit efficient discretization of complex modelling domains such as those containing topography, dipping layers and multiple scale structures. Iterative mesh refinement is guided by a goal-oriented error estimator that considers the relative error in the strike aligned fields and their spatial gradients, resulting in a more efficient mesh refinement than possible with a previous approach based on the absolute errors. Reliable error estimation is accomplished by a dual weighted residual method that is carried out via hierarchical basis computations. Our algorithm is parallelized over frequencies, wavenumbers, transmitters and receivers, where adaptive refinement is performed in parallel on subsets of these parameters. Mesh sharing allows an adapted mesh generated for a particular frequency and wavenumber to be shared with nearby frequencies and wavenumbers, thereby efficiently reducing the parallel load of the adaptive refinement calculations. We demonstrate the performance of our algorithm on a large cluster computer through scaling tests for a complex model that includes strong seafloor topography variations and multiple thin stacked hydrocarbon reservoirs. In tests using up to 800 processors and a realistic suite of CSEM data parameters, our algorithm obtained run-times as short as a few seconds to tens of seconds.