Matrix-Free Parallel Preconditioned Iterative Solvers for the 2D Helmholtz Equation Discretized with Finite Differences

We present a matrix-free parallel iterative solver for the Helmholtz equation related to applications in seismic problems and study its parallel performance. We apply Krylov subspace methods, GMRES, Bi-CGSTAB and IDR(s), to solve the linear system obtained from a second-order finite difference discretization. The Complex Shifted Laplace...

A matrix-free parallel solution method for the three-dimensional heterogeneous Helmholtz equation

The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the numerical solvers. For 3D large-scale applications, high-performance parallel solvers are also needed. In this...