Fast Parallel Solver of Time-harmonic Wave Equation with Topography

Designing a fast solver for the time-harmonic wave equation is a well-known challenging problem. However, when variable land and/or marine surface topography is present, the difficulty level increases even more. In this study, we have designed and investigated a novel scalable fast solver to tackle this problem. Our approach combines finite-element discretization, shifted-Laplacian preconditioner, and FFT. We have considered modeling examples with real topography from the Black Sea continental slope along with standard Salt and Overthrust benchmarks. Our observations have shown that our solver is highly efficient and scalable, indicating its practical applicability in geophysical modeling.