Fully Automatic, hp-Adaptive Simulations for Maxwell's Equations

摘要

The report describes a computational and theoretical work toward developing a fully automatic hp-adaptive methodology for solving 3D time- harmonic Maxwell equations. The algorithm produces automatically a sequence of hp meshes that deliver exponential convergence. The optimal hp-refinements are identified by minimizing the projection based interpolation error of the solution obtained on a (fine) grid obtained by a global hp- refinement of a current (coarse) grid. The idea of the algorithm is very general and it applies to all discretizations forming the hp de Rham diagram - Hi- H(curl)-and H(div)- conforming.