Search
Results
-
Dual Mesh Operator Preconditioning On 3D Screens: Low-Order Boundary Element Discretization
(2016)Research ReportReport -
-
Dispersion Analysis of Plane Wave Discontinuous Galerkin Methods
(2012)Research ReportThe plane wave discontinuous Galerkin (PWDG) method for the Helmholtz equation was introduced and analyzed in [Gittelson, C., Hiptmair, R., and Perugia, I. Plane wave discontinuous Galerkin methods: Analysis of the h-version. Math. Model. Numer. Anal. 43 (2009), 297–331] as a generalization of the so-called ultra-weak variational formulation, see [O. Cessenat and B. Despr´es, Application of an ultra weak variational formulation of elliptic ...Report -
Auxiliary Space Preconditioners for SIP-DG Discretizations of H(curl)-elliptic Problems with Discontinuous Coefficients
(2015)Research ReportWe propose a family of preconditioners for linear systems of equations arising from a piecewise polynomial symmetric Interior Penalty Discontinuous Galerkin (IP-DG) discretization of H(curl, )- elliptic boundary value problems on conforming meshes. The design and analysis of the proposed preconditioners relies on the auxiliary space method (ASM) employing an auxiliary space of H(curl, )- conforming finite element functions together with ...Report -
An A Priori Error Estimate for Interior Penalty Discretizations of the Curl-Curl Operator on Non-Conforming Meshes
(2014)Research ReportReport -
Plane Wave Discontinuous Galerkin Methods
(2013)Research ReportWe consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution ...Report -
-
Stabilized Galerkin for Transient Advection of Differential Forms
(2015)Research ReportWe deal with the discretization of generalized transient advection problems for differential forms on bounded spatial domains. We pursue an Eulerian method of lines approach with explicit time-stepping. Concerning spatial discretization we extend the jump stabilized Galerkin discretization proposed in [H. Heumann and R. Hiptmair, Stabilized Galerkin methods for magnetic advection, Math. Modelling Numer. Analysis, 47 (2013), pp. 1713–1732] ...Report -
Large deformation shape uncertainty quantification in acoustic scattering
(2015)Research ReportWe address shape uncertainty quantification for the two-dimensional Helmholtz trans- mission problem, where the shape of the scatterer is the only source of uncertainty. In the framework of the so-called deterministic approach, we provide a high-dimensional parametrization for the interface. Each domain configuration is mapped to a nominal configuration, obtaining a problem on a fixed domain with stochastic coefficients. To compute surrogate ...Report