Interior Point Methods for the Inverse Medium Problem on Massively Parallel Architectures

We consider the time-harmonic inverse medium problem, which finds many applications in science and engineering (e.g. optical tomography, seismic imaging, and non-destructive testing). It leads to large-scale non-convex PDE-constrained optimization problems and requires multiple solutions of notoriously difficult Helmholtz-type equations. A priori knowledge about the medium is also included through box constraints and thus avoid false solutions. The resulting nonconvex optimization problem is solved by a primal-dual interior-point algorithm, which is based on a full-space primal-dual approach to achieve feasibility and optimality simultaneously. It is combined with a sparse matrix factorization solver to attain a high level of performance and scalability on massively parallel architectures. We discuss the potential of the inversion method for a multi-layered inverse medium problem arising in seismic imaging and computational results are reported for seismic inversion examples on up to 1,024 cores of a Cray XE6.