Doctor of Philosophy, The Ohio State University, 2012, Electrical and Computer Engineering
This dissertation, investigates a discontinuous Galerkin (DG) methodology to solve Maxwell's equations in the time-domain.
More specifically, we focus on a Interior Penalty (IP) approach to derive a DG formulation. In general, discontinuous Galerkin methods decompose the computational domain into a number of disjoint polyhedral (elements). For each polyhedron, we define local basis functions and approximate the fields as a linear combination of these basis functions. To ensure equivalence to the original
problem the tangentially continuity of the electric and magnetic fields need to be enforced between polyhedra interfaces. This condition is applied in the weak sense by proper penalty terms on
the variational formulation also known as numerical fluxes.
Due to this way of coupling between adjacent polyhedra DG methods offer great flexibility and a nice set of properties such as, explicit time-marching, support for non-conformal meshes,
freedom in the choice of basis functions and high efficiency in parallelization. Here, we first introduce an Interior Penalty (IP) approach to derive a DG formulation and a physical interpretation of such an approach. This physical interpretation will provide a physical insight into the IP method and link important concepts like the duality pairing principle to a physical meaning. Furthermore, we discuss the time discretization and stability condition aspects of our scheme. Moreover, to address the issue of very small time steps in multi-scale applications we employ a local time-stepping (LTS) strategy which can greatly reduce the solution time. Secondly, we present an approach to incorporate a conformal Perfectly Matched Layer (PML) in our interior penalty discontinuous Galerkin time-domain (IPDGTD) framework. From a practical point of view, a conformal PML is easier to model compared to a Cartesian PML
and can reduce the buffer space between the structure and the
truncation boundary, thus potentially reducing the number of unkno (open full item for complete abstract)
Committee: Jin-Fa Lee (Advisor); Teixeira Fernando (Committee Member); Krishnamurthy Ashok (Committee Member)
Subjects: Electrical Engineering; Electromagnetics