An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation

Apreconditioner defined by an algebraicmultigrid cycle for a dampedHelmholtz operator is proposed for the Helmholtz equation. This approach is wellsuited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRESmethod are studiedwith linear, quadratic, and cubic finite element discretizations. Numerical experiments are performedwith two-dimensional problems describing acoustic scattering in a cross section of a car cabin and in a layeredmedium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower frequencies the growth is milder. The proposed preconditioner is particularly effective for low-frequency and mid-frequency problems.