A Geometric Multigrid Preconditioner for the Solution of the Helmholtz Equation in Three-Dimensional Heterogeneous Media on Massively Parallel Computers

We consider the numerical simulation of acoustic wave propagation in three-dimensional heterogeneous media as occcurring in seismic exploration. We focus on forward Helmholtz problems written in the frequency domain, since this setting is known to be particularly challenging for modern iterative methods. The geometric multigrid preconditioner proposed by Calandra et al. (Numer Linear Algebra Appl 20:663-688, 2013) is considered for the approximate solution of the Helmholtz equation at high frequencies in combination with dispersion minimizing finite difference methods. We present both a strong scalability study and a complexity analysis performed on a massively parallel distributed memory computer. Numerical results demonstrate the usefulness of the algorithm on a realistic three-dimensional application at high frequency.