About the multilevel method for solving the Helmholtz equation

Pascal Poullet
LAMIA, Université des Antilles, Guadeloupe

Classical methods to solve Helmholtz equation relying on incomplete factorization of shifted Laplacian operator provides attractive results but requires significant storage. Memory considerations are especially important when one needs to solve 3D problems. Multilevel schemes based on incremental unknowns have been introduced as an alternative with an efficiency in low and relatively high frequency regimes.
A new idea based on the adaptation of interpolation coefficients to plane waves allows to define new multilevel basis (Equation-based interpolation). The technique can be considered related to the multigrid method, using stencils based on the ideas stemming from a boundary element method. But the idea is also not too far from a domain decomposition technique.