Parallel Implementation of a Frequency-Domain Iterative Solver for 3D Acoustic Wave Equation

Summary We propose an iterative method for solving the Helmholtz equation in heterogeneous 3D media based on the usage of a Krylov-type technique with a semi-analytical preconditioner. The distinctive feature of our method is the use of the preconditioner, obtained as the solution of the complex damped Helmholtz equation in a 1D medium, where velocities vary only with depth. A matrix-by-vector multiplication of the preconditioned system is effectively evaluated via 2D FFT in lateral directions followed by solving of a number of small diagonal systems of linear algebraic equations (SLAE) in the vertical direction. We introduce a second level preconditioner based on the same concept which speeds up the convergence rate in a complex situation. Approach is adapted for high-performance computing systems with distributed memory.