On the numerical solution of a nonlinear stochastic Helmholtz equation with a multigrid preconditioner

摘要

We describe the use of a multigrid preconditioner to numerically solve a nonlinear stochastic Helmholtz-type equation. We implemented a computer code and carried out some analysis for a one-dimensional model problem in order to study the numerical method. In the case of the nonlinear stochastic one-dimensional model problem, a bifurcation in the solution was found. Numerical results are included to show the applicability of the method.