An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation

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.