The 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 ...

We consider the scattering of acoustic or electromagnetic waves at a penetrable object composed of different homogeneous materials. This problem can be recast as a firstkind boundary integral equation posed on the interface trace spaces through what we call a single trace boundary integral equation formulation (STF). Its Ritz-Galerkin discretization by means of low-order piecewise polynomial boundary elements on fine interface triangulations ...

The nonlinear spatially homogeneous integro-differential Boltzmann equation is a uniquely challenging task for numerical solvers due to the difficulty of efficiently computing the collision operator. A popular method is to expand the solution in Fourier modes and to truncate the collision operator. We present an approach based on the hyperbolic cross, whereby the performance can be greatly enhanced in some situations, as well as an offset ...