| Up until recently, the development and generalization of h-type and hp-type refinement techniques and strategies for the efficient and effective adaptive finite element analysis of continuum problems has been limited by the widespread use of geometrically conforming mesh discretizations, designed to maintain the continuity of the field model. These limits have retarded the growth, and restricted the potential, of modern adaptive finite element methods for engineering electromagnetic systems modeling, analysis and simulation. A new generalized theory and family of techniques which alleviate the need for conforming meshes is presented. The method is based on the concept of generalized irregular meshes and the formulation of a corresponding system of generalized constraint equations. Both theoretical and numerical investigations indicate that the new formulation can facilitate a very significant improvement in stable h-type and hp-type refinement flexibility, as well as, a strong potential for increased modeling efficiency and reduced computational costs.; The new techniques have been implemented and tested for 1D, 2D and 3D applications, for both scalar and vector finite element formulations in engineering electromagnetics. In addition, the new theory has been used to develop formulations for overlapping elements and layered meshes for adaptive error estimation; semi-full-domain elements for parallel and distributed processing domain decomposition methods; and, a new class of truly local and fully generalized hp -type finite elements for adaption. |
