Controllability techniques for the Helmholtz equation with spectral elements

We consider the use of controllability techniques to solve the Helmholtz equation. Instead of solving directly the time-harmonic equation, we return to the corresponding time-dependent equation and look for time-periodic solution. The convergence is accelerated with a control technique by representing the original time-harmonic equation as an...

A Flexible Solver of the Helmholtz Equation for Layered Media

A flexible solver for the Helmholtz equation is presented. The implementation of the solver is done in an object-oriented style, allowing for easy adaptation to different application problems. The solution methods that are employed are fast compared with standard solution techniques. The viability of the solver is demonstrated for realistic...

A preconditioner for the Helmholtz equation with perfectly matched layer

This paper discusses an iterative method for solving the Helmholtz equation with the perfectly matched layer (PML). The method consists of an outer and inner iteration process. The inner iteration is used to approximately solve a preconditioner, which in this case is based on a modified PML equation. The outer iteration is a Krylov subspace...

Algebraic Multilevel Preconditioning for Helmholtz Equation

We propose efficient algebraic multilevel preconditioning for the Helmholtz equation with high wave numbers. Our method is mainly based on using new multilevel ILU techniques for symmetric indefinite systems. The method is mainly based on three major ingredients: 1. symmetric maximum weight matchings to increase the block di- agonal dominance of...

Efficient Domain Decomposition Method for Acoustic Scattering in Multi-Layered Media

The time-harmonic acoustic scattering in multi-layered media is modeled with an inhomogeneous Helmholtz equation for the pressure field. For example, such problems result from acoustic geological surveys. The exterior problem is truncated into a rectangle and an absorbing boundary condition is posed on its boundaries. A low-order finite...

Preconditioning a Finite Element Solver of the Exterior Helmholtz Equation

We consider acoustic scattering about a general body. This is described by the Helmholtz equation exterior to the body. In order to truncate the infinite domain we use the BGT absorbing boundary condition. The resultant problem in a finite domain is solved by a finite element procedure. This yields a large sparse system of linear equations which...