Hybridization of finite element methods for the Helmholtz equation

P. Monk, University of Delaware, Newark, USA

Wednesday, April 30
at 16.15
in HG E1.2

When finite elements are applied to approximate the solution of the Helmholtz equation we are faced with the problem of solving a large sparse system that is neither Hermitian or positive definite (it is usually complex symmetric). Standard iterative methods become increasingly inefficient as the wave number increases. In particular multigrid methods are not optimal. In this talk we idiscuss the use of hybridized Raviart-Thomas finite elements and plane-wave methods for this problem. We show that one version of this scheme is equivalent to a discontinuous Galerkin method called the Ultra Weak Variational Formulation, and hence can be used to couple between standard elements and specialized plane wave elements. The resulting scheme shows promise in controlling the number of iterations of GMRES as the wave number increases.