Contributions to Books:
M. Huber, A. Pechstein, J. Schöberl:
"Hybrid Domain Decomposition Solvers for Scalar and Vectorial Wave Equation";
in: "Asc Report 15/2011",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
We present hybrid finite element methods, which are equivalent to a
discontinuous Galerkin method based on the ultra weak variational formu-
lation (UWVF) by Cessenat and Despres. When solving a scalar or vectorial
wave equation with hybrid finite elements, normal and tangential continu-
ity of the flux field, respectively, is broken across element interfaces and
reinforced again by introducing hybrid variables, which are supported only
on the element facets. Using this technique, coupling between degrees of
freedom belonging to the interior of different elements is avoided, and the
large number of volume unknowns on the element can be eliminated easily.
Consequently, the linear system of equations needs only to be solved for the
introduced facet degrees of freedom. It is shown by numerical experiments,
that iterative solvers using Schwarz preconditioners show good convergence
properties for these systems of equations.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.