Geometrically defined basis functions for polyhedral elements with applications to computational electromagnetics

Nedelec elements for computational electromagnetics

Polyhedral Finite Elements Using Harmonic Basis Functions

Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our poly...

Analytic approximations to Kelvin functions with applications to electromagnetics

We present analytical approximations for the real Kelvin function berx and the imaginary Kelvin function beix, using the two–point quasifractional approximation procedure. We have applied these approximations to the calculation of the current distribution within a cylindrical conductor. Our approximations are simple and accurate. The infinite number of roots is also obtained with the approximat...

Maximal elements of sub-topical functions with applications to global optimization

We study the support sets of sub-topical functions‎ ‎and investigate their maximal elements in order to establish a necessary and sufficient condition‎ ‎for the global minimum of the difference of two sub-topical functions‎.

Extremal Basis, Geometrically Separated Domains and Applications

In this paper we introduce the notion of extremal basis of tangent vector fields at a boundary point of finite type of a pseudo-convex domain in Cn, n ≥ 3. Using this notion we define the class of geometrically separated domains at a boundary point and we give a description of their complex geometry. Examples of such domains are given, for instance, by locally convex domains, domains with local...