First-order rooftop functions for the current discretisation in the method of moments solution of planar structures

Extends the classical zero-order rooftop functions with first-order rooftop functions. These functions are consistently linear, i.e. they yield a linear approximation of the surface current both inside each cell and along its sides. The authors discuss a general technique for the construction of first-order rooftop functions. These rooftop functions can be used very generally for the discretisation of an unknown complex vector function in the method of moments solution of integral equations. This is illustrated where the authors solve the electric field integral equation (EFIE) describing the microstrip discontinuity problem. The paper also presents some numerical results which illustrate the numerical convergence and the improved accuracy obtained with the first-order rooftop functions, when compared to the zero-order rooftop functions.