Computational and Applied Mathematics seminar

Abstract: We consider iterative methods for the Helmholtz equation that are based on the related time domain wave equation. In each iteration, the solution to the wave equation with a time-periodic forcing is computed and filtered in time. For Dirichlet and Neumann problems the iteration corresponds to a linear and coercive operator which, after discretization, is recast as a positive definite linear system of equations that can be solved with the conjugate gradient method. The main benefit of using these iterations comes when considering large scale problems. Implementing parallelized, high order methods that run efficiently on big computers is typically easier to do for time domain methods than for traditional Helmholtz solvers. We also show how the iterations can be used to turn a multiscale method for the wave equation into a multiscale method for the Helmholtz equation.