Abstract
This chapter presents the fundaments of the null-field method (NFM) for solving the Dirichlet and Neumann boundary-value problems. The chapter begins by showing that the scattering problem reduces to the approximation problem of the surface densities by convergent sequences. It then presents convergent projection methods for the general null-field equations. Next, it will investigate the conventional null-field method with discrete sources. The foundations of the method include convergence analysis following Ramm's treatment and derivation of sufficient conditions that guarantee the convergence of the approximate solution. The conclusion of this analysis is that the null-field method converges if the systems of expansion and testing functions form a Riesz basis in “L2(S).” Finally, it presents the equivalence between the null-field method and the auxiliary current method.
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