hp-Adaptive finite element methods for the Maxwell equations
09 / 2004 - 09 / 2009
Research questions: Construction of variable order edge/Discontinuous Galerkin finite elements for the Maxwell equations, which are suitable for hp-adaptation, satisfy the necessary div-curl constraints, and allow for anisotropic and non-linear materials. Development of stable and accurate, yet feasible time integration schemes for the Maxwell equations, which provide minimal dispersion and dissipation errors for electromagnetic waves. A-posteriori error analysis of the combined FEM and time integration techniques to obtain optimal control of mesh size and time step. Development of fast iterative eigenvalue and linear system solvers, which are suitable for the FEM discretizations of the Maxwell equations, developed in this project. Parallel numerical algorithms for optimal performance on parallel computers.