In this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution, which is expanded in a piecewise p-hierarchical basis. The key element in the strategy is an element-by-element criterion that controls the h- or p-refinement. Numerical results demonstrate both the simplicity and efficiency of the approach.

electromagnetic scattering, wire antenna, Pocklington, finite element approximations, hp-adaptivity"
Integro-ordinary differential equations (msc 45J05), Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (msc 65N30), Approximation by polynomials (msc 41A10), Antennas, wave-guides (msc 78A50)
Life Sciences (theme 5), Energy (theme 4), Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Lahaye, D.J.P, & Hemker, P.W. (2007). An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation. Modelling, Analysis and Simulation [MAS]. CWI.