A Discontinuous Galerkin Method for Simulations in Complex Domains

Abstract

In this report we present a new approach to simulations on complex shaped domains. The method uses a Discontinuous Galerkin discretization and a structured grid to construct the test and trial functions. Boundary and transmission conditions along the complex shape of the domains are imposed weakly via the Discontinuous Galerkin formulation. This method o ers a discretization where the minimal number of unknowns is independent of the possibly very complicated shape of the domain.