Degree and Wavenumber [In]dependence of Schwarz Preconditioner for the DPG Method [chapter]

Jay Gopalakrishnan, Joachim Schöberl
2015 Lecture Notes in Computational Science and Engineering  
This note describes an implementation of a discontinuous Petrov Galerkin (DPG) method for acoustic waves within the framework of high order finite elements provided by the software package NGSolve. A technique to impose the impedance boundary condition weakly is indicated. Numerical results from this implementation show that a multiplicative Schwarz algorithm, with no coarse solve, provides a p-preconditioner for solving the DPG system. The numerical observations suggest that the condition
more » ... r of the preconditioned system is independent of the frequency k and the polynomial degree p.
doi:10.1007/978-3-319-19800-2_22 fatcat:vwrl52pg6ncczmvk35lbabiita